From 720c46a2fcd3ce8f3fd93785caea84176ea2a788 Mon Sep 17 00:00:00 2001
From: root
 <root@hp-reasoning-b-pchanda-test-1node-8gpus-trainer-0.hp-reasoning-b-pchanda-test-1node-8gpus.bonete11.svc.cluster.local>
Date: Tue, 17 Feb 2026 04:35:18 +0000
Subject: [PATCH 01/11] add best of n sampling baselines + generate test
 baselines

---
 examples/TTSwithVerification/README.md        |  41 ++
 .../TTSwithVerification/bestofk_baseline.py   | 608 ++++++++++++++++++
 2 files changed, 649 insertions(+)
 create mode 100644 examples/TTSwithVerification/bestofk_baseline.py

diff --git a/examples/TTSwithVerification/README.md b/examples/TTSwithVerification/README.md
index ed7fbb4e..a2c52dd4 100644
--- a/examples/TTSwithVerification/README.md
+++ b/examples/TTSwithVerification/README.md
@@ -156,6 +156,39 @@ The Z3 solver handles diagonal directions (`Northwest`, `Northeast`, `Southwest`
 
 ---
 
+# Best-of-K Baseline
+
+A simple best-of-K baseline that generates K independent reasoning traces per example and selects the best based on:
+1. **Ground-truth matching** (default): Greedy selection of first correct answer among K samples
+2. **Critic model evaluation** (optional): Use a separate critic LLM to evaluate correctness without access to ground truth
+
+This baseline demonstrates that with sufficient sampling, even simple CoT can achieve good performance.
+
+## Usage
+
+```bash
+# Best-of-K with ground-truth evaluation
+python ./examples/TTSwithVerification/bestofk_baseline.py --task game24 -n 10 --k 4
+
+# Best-of-K with critic model evaluation
+python ./examples/TTSwithVerification/bestofk_baseline.py --task game24 -n 10 --k 4 --use_critic --critic_model Qwen/Qwen3-30B-A3B-Thinking-2507 --critic_port 8001
+```
+
+### Parameters
+
+| Argument | Description | Default |
+|----------|-------------|---------|
+| `--task` | Task: `game24`, `maze`, or `spatialmap` | required |
+| `--k` | Number of samples per example | `4` |
+| `--use_critic` | Use critic model for evaluation instead of ground truth | `False` |
+| `--critic_model` | Model to use for critic evaluation | MAIN_MODEL |
+| `--critic_port` | vLLM server port for critic model | `8001` |
+| `--num_examples`, `-n` | Number of examples to run | varies |
+| `--main_model` | Model for generation | `Qwen/Qwen3-30B-A3B-Thinking-2507` |
+| `--port` | vLLM server port for main model | `8000` |
+
+---
+
 ## Example Scripts
 
 Each script runs a full evaluation: loading a dataset, building structured prompts, running inference with step verification, and computing accuracy/token statistics.
@@ -169,6 +202,14 @@ python ./examples/TTSwithVerification/maze_stepverifier.py -n 1
 
 # SpatialMap with step verification
 python ./examples/TTSwithVerification/spatialmap_stepverifier.py -n 1
+
+# Best-of-K baseline (standard CoT, no monitors)
+python ./examples/TTSwithVerification/bestofk_baseline.py --task game24 -n 1 --k 4
+python ./examples/TTSwithVerification/bestofk_baseline.py --task maze -n 1 --k 4
+python ./examples/TTSwithVerification/bestofk_baseline.py --task spatialmap -n 1 --k 4
+
+# Best-of-K with critic model evaluation
+python ./examples/TTSwithVerification/bestofk_baseline.py --task game24 -n 1 --k 4 --use_critic
 ```
 
 ### Common arguments
diff --git a/examples/TTSwithVerification/bestofk_baseline.py b/examples/TTSwithVerification/bestofk_baseline.py
new file mode 100644
index 00000000..8864a38a
--- /dev/null
+++ b/examples/TTSwithVerification/bestofk_baseline.py
@@ -0,0 +1,608 @@
+import argparse
+import asyncio
+import json
+import logging
+import os
+import re
+from dataclasses import dataclass
+from typing import List, Optional
+
+import numpy as np
+from datasets import load_dataset
+from tqdm import tqdm
+from transformers import AutoTokenizer
+
+from interwhen import stream_completion
+
+# ============== MODEL CONFIGURATION ==============
+MAIN_MODEL = "Qwen/Qwen3-30B-A3B-Thinking-2507"
+# =================================================
+
+logger = logging.getLogger(__name__)
+
+
+@dataclass
+class SampleResult:
+    output: str
+    correct: bool
+    extracted: Optional[str]
+    message: str
+    tokens: int
+    critic_correct: Optional[bool] = None
+
+
+def get_model_short_name(model_name: str) -> str:
+    short_name = model_name.split("/")[-1]
+    return short_name.replace(" ", "_").replace(":", "-")
+
+
+def get_output_dirs(task: str, main_model: str, base_dir: str = "../../b-pchanda/Outputs_TTS/BestOfKResults"):
+    model_short_name = get_model_short_name(main_model)
+    output_base = os.path.join(base_dir, task, model_short_name)
+    dirs = {
+        "base": output_base,
+        "reasoning": os.path.join(output_base, "Reasoning_output"),
+    }
+    for dir_path in dirs.values():
+        os.makedirs(dir_path, exist_ok=True)
+    return dirs
+
+
+def init_llm_server(model_name, max_tokens=32768, port=8000, temperature=0.6, seed=42):
+    url = f"http://localhost:{port}/v1/completions"
+    payload = {
+        "model": model_name,
+        "max_tokens": max_tokens,
+        "top_k": 20,
+        "top_p": 0.95,
+        "min_p": 0.0,
+        "do_sample": True,
+        "temperature": temperature,
+        "stream": True,
+        "logprobs": 20,
+        "use_beam_search": False,
+        "prompt_cache": True,
+        "seed": seed,
+    }
+    headers = {"Content-Type": "application/json"}
+    return {"url": url, "payload": payload, "headers": headers}
+
+
+def count_tokens(text: str, tokenizer) -> int:
+    tokens = tokenizer.encode(text, add_special_tokens=False)
+    return len(tokens)
+
+
+def save_outputs(idx: int, outputs: List[SampleResult], best_idx: int, output_dir: str):
+    os.makedirs(output_dir, exist_ok=True)
+    filepath = os.path.join(output_dir, f"output_{idx}.txt")
+    with open(filepath, "w", encoding="utf-8") as f:
+        f.write(f"BEST_INDEX={best_idx}\n")
+        for i, result in enumerate(outputs):
+            f.write("\n" + "=" * 80 + "\n")
+            f.write(f"SAMPLE {i}\n")
+            f.write(f"CORRECT={result.correct}\n")
+            f.write(f"CRITIC_CORRECT={result.critic_correct}\n")
+            f.write(f"EXTRACTED={result.extracted}\n")
+            f.write(f"TOKENS={result.tokens}\n")
+            f.write(f"MESSAGE={result.message}\n")
+            f.write("\n")
+            f.write(result.output)
+            f.write("\n")
+    logger.info(f"Saved outputs to {filepath}")
+
+
+# --------------------- Game24 helpers ---------------------
+
+def build_game24_prompt(nums):
+    a, b, c, d = nums
+    boxed = r"\\boxed{}"
+    base_prompt = f"""
+You are solving the Game of 24.
+
+You are given four numbers: {a}, {b}, {c}, {d}
+
+Your job is to produce a valid arithmetic expression using:
+- ALL four numbers exactly once
+- ONLY +, -, *, /
+- The expression must evaluate to exactly 24.
+
+Please reason step by step, and put your final answer containing only the expression within {boxed}.
+""".strip()
+    return base_prompt
+
+
+def extract_solution_game24(text):
+    boxed_pattern = r"\\boxed\{"
+    matches = list(re.finditer(boxed_pattern, text))
+    if not matches:
+        return None
+    last_match = matches[-1]
+    start = last_match.end()
+    brace_count = 1
+    end = start
+    while end < len(text) and brace_count > 0:
+        if text[end] == "{":
+            brace_count += 1
+        elif text[end] == "}":
+            brace_count -= 1
+        end += 1
+    expr = text[start:end - 1].strip()
+
+    frac_pattern = r"\\frac\{([^{}]+)\}\{([^{}]+)\}"
+    while re.search(frac_pattern, expr):
+        expr = re.sub(frac_pattern, r"(\1/\2)", expr)
+
+    replacements = {
+        r"\times": "*",
+        r"\cdot": "*",
+        r"\div": "/",
+    }
+    for latex, op in replacements.items():
+        expr = expr.replace(latex, op)
+
+    expr = expr.replace(r"\\,", "").replace(r"\\ ", "")
+    expr = re.sub(r"\)\s*\(", ")*(", expr)
+    expr = re.sub(r"\)\s*(\d)", r")*\1", expr)
+    expr = re.sub(r"(\d)\s*\(", r"\1*(", expr)
+
+    return expr
+
+
+def extract_numbers_from_expr(expr):
+    numbers = re.findall(r"\d+\.?\d*", expr)
+    return [int(float(n)) if float(n).is_integer() else float(n) for n in numbers]
+
+
+def validate_numbers_used(expr, expected_nums):
+    used_nums = extract_numbers_from_expr(expr)
+    return sorted(used_nums) == sorted(expected_nums)
+
+
+def evaluate_expression(expr, expected_nums=None):
+    try:
+        if expected_nums is not None and not validate_numbers_used(expr, expected_nums):
+            return False
+        value = eval(expr, {"__builtins__": None}, {})
+        return abs(value - 24) < 1e-6
+    except Exception:
+        return False
+
+
+def evaluate_game24_answer(answer, nums):
+    expr = extract_solution_game24(answer)
+    if not expr:
+        return False, None, "No expression found"
+    if evaluate_expression(expr, expected_nums=nums):
+        return True, expr, "Correct solution (evaluates to 24 using exactly the given numbers)"
+    used_nums = extract_numbers_from_expr(expr)
+    if sorted(used_nums) != sorted(nums):
+        return False, expr, f"Incorrect: Expression uses {used_nums}, expected {nums}"
+    return False, expr, "Expression does not evaluate to 24"
+
+
+# --------------------- Maze/SpatialMap helpers ---------------------
+
+def remove_last_paragraph(s: str) -> str:
+    return s[:-143] if len(s) > 143 else s
+
+
+def build_maze_prompt(example):
+    pre_prompt = (
+        "You are an expert problem solver. Carefully read the following multiple-choice question "
+        "and think through the solution step-by-step before providing your final answer. "
+        "Provide your final answer option by enclosing it within \\boxed{A/B/C/D}.:"
+    )
+    description = remove_last_paragraph(str(example.get("prompt")))
+    return pre_prompt, description
+
+
+def build_spatialmap_prompt(example):
+    pre_prompt = (
+        "You are an expert problem solver. Carefully read the following multiple-choice question "
+        "and think through the solution step-by-step before providing your final answer." 
+        "Provide your final answer option by enclosing it within \\boxed{A/B/C/D}.:"
+    )
+    description = remove_last_paragraph(str(example.get("prompt")))
+    return pre_prompt, description
+
+
+def extract_solution_mcq(text):
+    matches = re.findall(r"\\boxed\{([^}]*)\}", text)
+    if not matches:
+        return None
+    expr = matches[-1].strip()
+    choice_match = re.search(r"\b([ABCD])\b", expr, flags=re.IGNORECASE)
+    if not choice_match:
+        return None
+    return choice_match.group(1).upper()
+
+
+def extract_options_from_prompt(prompt_text, target_options):
+    pattern = r"\b([A-D])\.\s*(.*?)(?=\s*[A-D]\.\s*|$)"
+    raw = re.findall(pattern, prompt_text, flags=re.DOTALL)
+    options = {k: v.strip().rstrip(".") for k, v in raw}
+    if target_options:
+        options = {k: v for k, v in options.items() if k in target_options}
+    return options
+
+
+def evaluate_mcq_answer(answer, options, ground_truth):
+    sol = extract_solution_mcq(answer)
+    gt_sol = str(ground_truth).strip()
+    if not sol:
+        return False, None, "No expression found"
+    sol = sol.strip()
+    if sol in options:
+        if options[sol] == gt_sol:
+            return True, sol, f"Correct: option {sol} -> {options[sol]}"
+        return False, sol, f"Incorrect: expected '{gt_sol}', got '{options[sol]}' (option {sol})"
+    if sol.lower() == gt_sol.lower():
+        return True, sol, f"Correct: answer text matches ground truth: {sol}"
+    for opt_letter, opt_value in options.items():
+        if sol.lower() == opt_value.lower():
+            if opt_value == gt_sol:
+                return True, sol, f"Correct: answer text {sol} (option {opt_letter})"
+            return False, sol, f"Incorrect: expected '{gt_sol}', got '{opt_value}' (option {opt_letter})"
+    return False, sol, f"Solution '{sol}' not found in options or ground truth"
+
+
+def build_full_prompt(task, example, nums=None):
+    if task == "game24":
+        prompt = build_game24_prompt(nums)
+        return f"<|im_start|>user\n{prompt}<|im_end|>\n<|im_start|>assistant\n"
+    if task == "maze":
+        system_prompt, user_prompt = build_maze_prompt(example)
+    else:
+        system_prompt, user_prompt = build_spatialmap_prompt(example)
+    return (
+        f"<|im_start|>system\n{system_prompt}<|im_end|>\n"
+        f"<|im_start|>user\n{user_prompt}<|im_end|>\n"
+        f"<|im_start|>assistant\n"
+    )
+
+
+def load_dataset_for_task(task):
+    if task == "game24":
+        return load_dataset("nlile/24-game", split="train")
+    if task == "maze":
+        return load_dataset("microsoft/VISION_LANGUAGE", "maze", split="val")
+    if task == "spatialmap":
+        return load_dataset("microsoft/VISION_LANGUAGE", "spatial_map_text_only", split="val")
+    raise ValueError(f"Unsupported task: {task}")
+
+
+def resolve_indices(task, dataset_len, args):
+    if args.indices:
+        return [int(x.strip()) for x in args.indices.split(",")]
+    if args.xrange:
+        parts = args.xrange.split("-")
+        if len(parts) == 2:
+            try:
+                start = int(parts[0].strip())
+                end = int(parts[1].strip())
+                return range(start, end)
+            except ValueError:
+                raise ValueError(f"Invalid xrange format: {args.xrange}. Use 'start-end'")
+    if args.num_examples:
+        return np.linspace(0, dataset_len - 1, args.num_examples, dtype=int)
+    # Default: use full range
+    start = args.start if args.start is not None else 0
+    end = args.end if args.end is not None else dataset_len
+    return range(start, end)
+
+
+def run_k_samples(prompt, llm_server, k, seed):
+    outputs = []
+    for i in range(k):
+        llm_server["payload"]["seed"] = seed + i
+        outputs.append(asyncio.run(stream_completion(
+            prompt,
+            llm_server=llm_server,
+            monitors=(),
+            add_delay=False,
+            termination_requires_validation=False,
+            async_execution=True,
+        )))
+    return outputs
+
+
+# --------------------- Critic model helpers ---------------------
+
+def build_game24_critic_prompt(nums, reasoning_output):
+    """Build critic prompt to evaluate Game of 24 solution."""
+    return f"""You are a math verifier. Evaluate the following Game of 24 solution.
+
+Numbers: {nums}
+Target: 24
+
+Student's reasoning and answer:
+{reasoning_output}
+
+Verify:
+1. Does it use ALL four numbers exactly once?
+2. Does each step follow correct arithmetic?
+3. Does the final expression evaluate to exactly 24?
+
+Respond with ONLY: "CORRECT" or "INCORRECT"
+"""
+
+
+def build_mcq_critic_prompt(task, task_description, reasoning_output):
+    """Build critic prompt to evaluate MCQ solution."""
+    task_name = "Maze" if task == "maze" else "Spatial Reasoning"
+    return f"""You are an expert {task_name} verifier. Evaluate the following solution.
+
+Task:
+{task_description}
+
+Student's reasoning and answer:
+{reasoning_output}
+
+Verify the correctness of the step-by-step reasoning and final answer.
+
+Respond with ONLY: "CORRECT" or "INCORRECT"
+"""
+
+
+async def evaluate_with_critic(output_text, task, example, critic_llm_server, tokenizer, nums=None):
+    """Use critic model to evaluate correctness of output."""
+    try:
+        if task == "game24":
+            critic_prompt = build_game24_critic_prompt(nums, output_text)
+        else:
+            if task == "maze":
+                _, task_desc = build_maze_prompt(example)
+            else:
+                _, task_desc = build_spatialmap_prompt(example)
+            critic_prompt = build_mcq_critic_prompt(task, task_desc, output_text)
+        
+        critic_system = "You are a strict academic verifier."
+        full_prompt = f"<|im_start|>system\n{critic_system}<|im_end|>\n<|im_start|>user\n{critic_prompt}<|im_end|>\n<|im_start|>assistant\n"
+        
+        critic_output = await stream_completion(
+            full_prompt,
+            llm_server=critic_llm_server,
+            monitors=(),
+            add_delay=False,
+            termination_requires_validation=False,
+            async_execution=True,
+        )
+        
+        is_correct = "CORRECT" in critic_output.upper()
+        return is_correct, critic_output
+    except Exception as e:
+        logger.warning(f"Critic evaluation failed: {e}")
+        return False, ""
+
+
+def run_k_samples_with_critic(
+    prompt,
+    llm_server,
+    critic_llm_server,
+    k,
+    seed,
+    task,
+    example,
+    tokenizer,
+    eval_fn,
+    nums=None,
+    early_stop=False,
+):
+    """Run up to K samples, evaluate with critic, and score with ground truth."""
+    sample_results = []
+    for i in range(k):
+        llm_server["payload"]["seed"] = seed + i
+        output = asyncio.run(stream_completion(
+            prompt,
+            llm_server=llm_server,
+            monitors=(),
+            add_delay=False,
+            termination_requires_validation=False,
+            async_execution=True,
+        ))
+
+        critic_correct, critic_response = asyncio.run(evaluate_with_critic(
+            output, task, example, critic_llm_server, tokenizer, nums=nums
+        ))
+        is_correct, extracted, message = eval_fn(output)
+        token_count = count_tokens(output, tokenizer)
+
+        sample_results.append(SampleResult(
+            output=output,
+            correct=is_correct,
+            extracted=extracted,
+            message=f"Critic verdict: {'CORRECT' if critic_correct else 'INCORRECT'} | {message}",
+            tokens=token_count,
+            critic_correct=critic_correct,
+        ))
+
+        if early_stop and critic_correct:
+            break
+
+    return sample_results
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser(description="Best-of-K baseline (standard CoT) for TTSwithVerification datasets")
+    parser.add_argument("--task", type=str, required=True, choices=["game24", "maze", "spatialmap"],
+                        help="Task to run")
+    parser.add_argument("--k", type=int, default=4, help="Number of samples per example")
+    parser.add_argument("--num_examples", "-n", type=int, default=None,
+                        help="Number of examples to run (overrides start/end)")
+    parser.add_argument("--indices", type=str, default=None,
+                        help="Comma-separated indices to run")
+    parser.add_argument("--xrange", type=str, default=None,
+                        help="Range of indices to run (format: 'start-end')")
+    parser.add_argument("--start", type=int, default=None, help="Start index")
+    parser.add_argument("--end", type=int, default=None, help="End index")
+    parser.add_argument("--main_model", type=str, default=MAIN_MODEL, help="Main model to use for generation")
+    parser.add_argument("--port", type=int, default=8000, help="vLLM server port")
+    parser.add_argument("--use_critic", action="store_true", help="Use critic model for evaluation instead of ground truth")
+    parser.add_argument("--critic_model", type=str, default=MAIN_MODEL, help="Critic model to use for evaluation")
+    parser.add_argument("--critic_port", type=int, default=8000, help="vLLM server port for critic model (default: same as main model port)")
+    parser.add_argument("--critic_early_stop", action="store_true", help="Stop sampling after first critic-correct trace")
+    parser.add_argument("--seed", type=int, default=42, help="Base random seed")
+    parser.add_argument("--max_tokens", type=int, default=32768, help="Max tokens for generation")
+    parser.add_argument("--temperature", type=float, default=0.6, help="Sampling temperature")
+    parser.add_argument("--debug", "-d", action="store_true", help="Enable debug logging")
+    args = parser.parse_args()
+
+    log_level = logging.DEBUG if args.debug else logging.INFO
+    logging.basicConfig(level=log_level, format="%(message)s")
+
+
+    dataset = load_dataset_for_task(args.task)
+    indices = resolve_indices(args.task, len(dataset), args)
+
+    llm_server = init_llm_server(
+        args.main_model,
+        max_tokens=args.max_tokens,
+        port=args.port,
+        temperature=args.temperature,
+        seed=args.seed,
+    )
+
+    critic_llm_server = None
+    if args.use_critic:
+        critic_llm_server = init_llm_server(
+            args.critic_model,
+            max_tokens=512,
+            port=args.critic_port,
+            temperature=0.2,
+            seed=args.seed,
+        )
+        logger.info(f"Using critic model: {args.critic_model} on port {args.critic_port}")
+
+    logger.info(f"Loading tokenizer for {args.main_model}...")
+    tokenizer = AutoTokenizer.from_pretrained(args.main_model, trust_remote_code=True)
+    logger.info("Tokenizer loaded successfully.")
+
+    output_dirs = get_output_dirs(args.task, args.main_model)
+
+    total_examples = 0
+    total_correct = 0
+    total_correct_samples = 0
+    total_samples = 0
+    critic_correct_samples = 0
+    critic_total_samples = 0
+    total_tokens = 0
+    total_tokens_all_samples = 0
+    results = []
+
+    for idx in tqdm(indices, desc="Processing examples", unit="example"):
+        example = dataset[int(idx)]
+        if args.task == "game24":
+            nums = example["numbers"]
+            prompt = build_full_prompt(args.task, example, nums=nums)
+            eval_fn = lambda output: evaluate_game24_answer(output, nums)
+            options = None
+        else:
+            prompt = build_full_prompt(args.task, example)
+            gt = str(example.get("ground_truth", "")).strip()
+            if gt == "Q4":
+                target_options = ["A", "B"]
+            else:
+                target_options = ["A", "B", "C", "D"]
+            if args.task == "maze":
+                _, user_prompt = build_maze_prompt(example)
+            else:
+                _, user_prompt = build_spatialmap_prompt(example)
+            options = extract_options_from_prompt(user_prompt, target_options)
+            eval_fn = lambda output: evaluate_mcq_answer(output, options, gt)
+
+        logger.info(f"---- Example {idx} ----")
+        
+        if args.use_critic:
+            sample_results = run_k_samples_with_critic(
+                prompt, llm_server, critic_llm_server, args.k, args.seed,
+                args.task, example, tokenizer, eval_fn, nums=(nums if args.task == "game24" else None),
+                early_stop=args.critic_early_stop
+            )
+        else:
+            outputs = run_k_samples(prompt, llm_server, args.k, args.seed)
+            sample_results = []
+            for output in outputs:
+                is_correct, extracted, message = eval_fn(output)
+                token_count = count_tokens(output, tokenizer)
+                sample_results.append(SampleResult(
+                    output=output,
+                    correct=is_correct,
+                    extracted=extracted,
+                    message=message,
+                    tokens=token_count,
+                    critic_correct=None,
+                ))
+
+        if args.use_critic:
+            best_idx = next((i for i, r in enumerate(sample_results) if r.critic_correct), 0)
+        else:
+            best_idx = next((i for i, r in enumerate(sample_results) if r.correct), 0)
+        best_result = sample_results[best_idx]
+        any_correct = any(r.correct for r in sample_results)
+        correct_samples = sum(1 for r in sample_results if r.correct)
+        critic_correct_samples_example = sum(1 for r in sample_results if r.critic_correct)
+
+        save_outputs(idx, sample_results, best_idx, output_dirs["reasoning"])
+
+        total_examples += 1
+        if any_correct:
+            total_correct += 1
+        total_correct_samples += correct_samples
+        total_samples += len(sample_results)
+        critic_correct_samples += critic_correct_samples_example
+        critic_total_samples += len(sample_results)
+        total_tokens += best_result.tokens
+        total_tokens_all_samples += sum(r.tokens for r in sample_results)
+
+        results.append({
+            "idx": int(idx),
+            "best_idx": best_idx,
+            "any_correct": any_correct,
+            "best_correct": best_result.correct,
+            "best_critic_correct": best_result.critic_correct,
+            "best_extracted": best_result.extracted,
+            "best_message": best_result.message,
+            "best_tokens": best_result.tokens,
+            "all_tokens": [r.tokens for r in sample_results],
+            "all_correct": [r.correct for r in sample_results],
+            "all_critic_correct": [r.critic_correct for r in sample_results],
+            "options": options,
+        })
+
+        logger.info(f"Best sample: {best_idx} | Correct in K: {any_correct}")
+        logger.info(f"Best message: {best_result.message}")
+
+    accuracy = total_correct / total_examples if total_examples else 0
+    avg_best_tokens = total_tokens / total_examples if total_examples else 0
+    avg_all_tokens = total_tokens_all_samples / total_examples if total_examples else 0
+
+    summary = {
+        "task": args.task,
+        "model": args.main_model,
+        "k": args.k,
+        "use_critic": args.use_critic,
+        "total_examples": total_examples,
+        "correct": total_correct,
+        "correct_samples": total_correct_samples,
+        "total_samples": total_samples,
+        "critic_correct_samples": critic_correct_samples,
+        "critic_total_samples": critic_total_samples,
+        "critic_accuracy": (critic_correct_samples / critic_total_samples) if critic_total_samples else 0,
+        "accuracy": accuracy,
+        "avg_best_tokens": avg_best_tokens,
+        "avg_all_tokens": avg_all_tokens,
+        "total_tokens_best": total_tokens,
+        "total_tokens_all_samples": total_tokens_all_samples,
+        "results": results,
+    }
+    
+    if args.use_critic:
+        summary["critic_model"] = args.critic_model
+        summary["critic_port"] = args.critic_port
+        summary["critic_early_stop"] = args.critic_early_stop
+
+    summary_path = os.path.join(output_dirs["base"], "summary.json")
+    with open(summary_path, "w", encoding="utf-8") as f:
+        json.dump(summary, f, indent=2)
+    logger.info(f"Saved summary to {summary_path}")

From bfc7d774b372b9d67f8240892408bccb48cca16a Mon Sep 17 00:00:00 2001
From: Prateek Chanda <prateekkol21@gmail.com>
Date: Fri, 20 Feb 2026 04:49:21 +0000
Subject: [PATCH 02/11] add fixes

---
 .../TTSwithVerification/bestofk_baseline.py   | 119 ++++++++++++++++--
 1 file changed, 106 insertions(+), 13 deletions(-)

diff --git a/examples/TTSwithVerification/bestofk_baseline.py b/examples/TTSwithVerification/bestofk_baseline.py
index 8864a38a..0a1a0c18 100644
--- a/examples/TTSwithVerification/bestofk_baseline.py
+++ b/examples/TTSwithVerification/bestofk_baseline.py
@@ -29,6 +29,7 @@ class SampleResult:
     message: str
     tokens: int
     critic_correct: Optional[bool] = None
+    critic_feedback: Optional[str] = None
 
 
 def get_model_short_name(model_name: str) -> str:
@@ -86,6 +87,8 @@ def save_outputs(idx: int, outputs: List[SampleResult], best_idx: int, output_di
             f.write(f"EXTRACTED={result.extracted}\n")
             f.write(f"TOKENS={result.tokens}\n")
             f.write(f"MESSAGE={result.message}\n")
+            if result.critic_feedback:
+                f.write(f"CRITIC_FEEDBACK={result.critic_feedback}\n")
             f.write("\n")
             f.write(result.output)
             f.write("\n")
@@ -292,25 +295,31 @@ def resolve_indices(task, dataset_len, args):
     return range(start, end)
 
 
-def run_k_samples(prompt, llm_server, k, seed):
-    outputs = []
+async def run_k_samples_async(prompt, llm_server, k, seed):
+    """Parallelized version - runs all k samples concurrently."""
+    tasks = []
     for i in range(k):
         llm_server["payload"]["seed"] = seed + i
-        outputs.append(asyncio.run(stream_completion(
+        tasks.append(stream_completion(
             prompt,
             llm_server=llm_server,
             monitors=(),
             add_delay=False,
             termination_requires_validation=False,
             async_execution=True,
-        )))
-    return outputs
+        ))
+    return await asyncio.gather(*tasks)
+
+
+def run_k_samples(prompt, llm_server, k, seed):
+    """Wrapper to run parallelized k samples."""
+    return asyncio.run(run_k_samples_async(prompt, llm_server, k, seed))
 
 
 # --------------------- Critic model helpers ---------------------
 
 def build_game24_critic_prompt(nums, reasoning_output):
-    """Build critic prompt to evaluate Game of 24 solution."""
+    """Build critic prompt to evaluate Game of 24 solution and provide reasoning."""
     return f"""You are a math verifier. Evaluate the following Game of 24 solution.
 
 Numbers: {nums}
@@ -324,12 +333,17 @@ def build_game24_critic_prompt(nums, reasoning_output):
 2. Does each step follow correct arithmetic?
 3. Does the final expression evaluate to exactly 24?
 
-Respond with ONLY: "CORRECT" or "INCORRECT"
+Respond in the following format:
+VERDICT: CORRECT or INCORRECT
+REASONING: Your detailed explanation
+
+If CORRECT, briefly explain why.
+If INCORRECT, explain what went wrong and how to fix it.
 """
 
 
 def build_mcq_critic_prompt(task, task_description, reasoning_output):
-    """Build critic prompt to evaluate MCQ solution."""
+    """Build critic prompt to evaluate MCQ solution and provide reasoning."""
     task_name = "Maze" if task == "maze" else "Spatial Reasoning"
     return f"""You are an expert {task_name} verifier. Evaluate the following solution.
 
@@ -341,12 +355,17 @@ def build_mcq_critic_prompt(task, task_description, reasoning_output):
 
 Verify the correctness of the step-by-step reasoning and final answer.
 
-Respond with ONLY: "CORRECT" or "INCORRECT"
+Respond in the following format:
+VERDICT: CORRECT or INCORRECT
+REASONING: Your detailed explanation
+
+If CORRECT, briefly explain why.
+If INCORRECT, explain what went wrong and suggest the correct approach.
 """
 
 
 async def evaluate_with_critic(output_text, task, example, critic_llm_server, tokenizer, nums=None):
-    """Use critic model to evaluate correctness of output."""
+    """Use critic model to evaluate correctness of output and extract reasoning feedback."""
     try:
         if task == "game24":
             critic_prompt = build_game24_critic_prompt(nums, output_text)
@@ -370,7 +389,15 @@ async def evaluate_with_critic(output_text, task, example, critic_llm_server, to
         )
         
         is_correct = "CORRECT" in critic_output.upper()
-        return is_correct, critic_output
+        
+        # Extract reasoning from verdict and reasoning format
+        reasoning = ""
+        if "REASONING:" in critic_output:
+            reasoning = critic_output.split("REASONING:", 1)[1].strip()
+        elif "VERDICT:" not in critic_output:
+            reasoning = critic_output
+        
+        return is_correct, reasoning
     except Exception as e:
         logger.warning(f"Critic evaluation failed: {e}")
         return False, ""
@@ -390,6 +417,22 @@ def run_k_samples_with_critic(
     early_stop=False,
 ):
     """Run up to K samples, evaluate with critic, and score with ground truth."""
+    if early_stop:
+        # Sequential execution for early stopping
+        return _run_k_samples_with_critic_sequential(
+            prompt, llm_server, critic_llm_server, k, seed, task, example, tokenizer, eval_fn, nums
+        )
+    else:
+        # Parallelized execution when not using early stopping
+        return asyncio.run(_run_k_samples_with_critic_parallel(
+            prompt, llm_server, critic_llm_server, k, seed, task, example, tokenizer, eval_fn, nums
+        ))
+
+
+def _run_k_samples_with_critic_sequential(
+    prompt, llm_server, critic_llm_server, k, seed, task, example, tokenizer, eval_fn, nums=None
+):
+    """Sequential version - required for early stopping."""
     sample_results = []
     for i in range(k):
         llm_server["payload"]["seed"] = seed + i
@@ -402,7 +445,7 @@ def run_k_samples_with_critic(
             async_execution=True,
         ))
 
-        critic_correct, critic_response = asyncio.run(evaluate_with_critic(
+        critic_correct, critic_feedback = asyncio.run(evaluate_with_critic(
             output, task, example, critic_llm_server, tokenizer, nums=nums
         ))
         is_correct, extracted, message = eval_fn(output)
@@ -415,14 +458,60 @@ def run_k_samples_with_critic(
             message=f"Critic verdict: {'CORRECT' if critic_correct else 'INCORRECT'} | {message}",
             tokens=token_count,
             critic_correct=critic_correct,
+            critic_feedback=critic_feedback,
         ))
 
-        if early_stop and critic_correct:
+        if critic_correct:
             break
 
     return sample_results
 
 
+async def _run_k_samples_with_critic_parallel(
+    prompt, llm_server, critic_llm_server, k, seed, task, example, tokenizer, eval_fn, nums=None
+):
+    """Parallelized version - runs all k samples concurrently and evaluates with critic."""
+    # Step 1: Generate all outputs in parallel
+    output_tasks = []
+    for i in range(k):
+        llm_server["payload"]["seed"] = seed + i
+        output_tasks.append(stream_completion(
+            prompt,
+            llm_server=llm_server,
+            monitors=(),
+            add_delay=False,
+            termination_requires_validation=False,
+            async_execution=True,
+        ))
+    outputs = await asyncio.gather(*output_tasks)
+
+    # Step 2: Evaluate all outputs in parallel
+    evaluation_tasks = []
+    for output in outputs:
+        evaluation_tasks.append(evaluate_with_critic(
+            output, task, example, critic_llm_server, tokenizer, nums=nums
+        ))
+    critic_evaluations = await asyncio.gather(*evaluation_tasks)
+
+    # Step 3: Compile results
+    sample_results = []
+    for output, (critic_correct, critic_feedback) in zip(outputs, critic_evaluations):
+        is_correct, extracted, message = eval_fn(output)
+        token_count = count_tokens(output, tokenizer)
+
+        sample_results.append(SampleResult(
+            output=output,
+            correct=is_correct,
+            extracted=extracted,
+            message=f"Critic verdict: {'CORRECT' if critic_correct else 'INCORRECT'} | {message}",
+            tokens=token_count,
+            critic_correct=critic_correct,
+            critic_feedback=critic_feedback,
+        ))
+
+    return sample_results
+
+
 if __name__ == "__main__":
     parser = argparse.ArgumentParser(description="Best-of-K baseline (standard CoT) for TTSwithVerification datasets")
     parser.add_argument("--task", type=str, required=True, choices=["game24", "maze", "spatialmap"],
@@ -442,6 +531,7 @@ def run_k_samples_with_critic(
     parser.add_argument("--critic_model", type=str, default=MAIN_MODEL, help="Critic model to use for evaluation")
     parser.add_argument("--critic_port", type=int, default=8000, help="vLLM server port for critic model (default: same as main model port)")
     parser.add_argument("--critic_early_stop", action="store_true", help="Stop sampling after first critic-correct trace")
+    parser.add_argument("--critic_feedback_baseline", action="store_true", help="Use critic feedback as a separate baseline for post-hoc correction")
     parser.add_argument("--seed", type=int, default=42, help="Base random seed")
     parser.add_argument("--max_tokens", type=int, default=32768, help="Max tokens for generation")
     parser.add_argument("--temperature", type=float, default=0.6, help="Sampling temperature")
@@ -563,10 +653,12 @@ def run_k_samples_with_critic(
             "best_critic_correct": best_result.critic_correct,
             "best_extracted": best_result.extracted,
             "best_message": best_result.message,
+            "best_critic_feedback": best_result.critic_feedback,
             "best_tokens": best_result.tokens,
             "all_tokens": [r.tokens for r in sample_results],
             "all_correct": [r.correct for r in sample_results],
             "all_critic_correct": [r.critic_correct for r in sample_results],
+            "all_critic_feedback": [r.critic_feedback for r in sample_results],
             "options": options,
         })
 
@@ -601,6 +693,7 @@ def run_k_samples_with_critic(
         summary["critic_model"] = args.critic_model
         summary["critic_port"] = args.critic_port
         summary["critic_early_stop"] = args.critic_early_stop
+        summary["critic_feedback_baseline"] = args.critic_feedback_baseline
 
     summary_path = os.path.join(output_dirs["base"], "summary.json")
     with open(summary_path, "w", encoding="utf-8") as f:

From fb28eba2e6e4bd52eabf3f32ddd1eaa0771f7ad5 Mon Sep 17 00:00:00 2001
From: Prateek Chanda <prateekkol21@gmail.com>
Date: Sat, 21 Feb 2026 09:15:56 +0000
Subject: [PATCH 03/11] add multiprocess vllm setup and ignore outputs

---
 .gitignore                                    |   2 +
 .../MULTIPROCESS_README.md                    |  67 +++
 .../TTSwithVerification/bestofk_baseline.py   | 493 +++++++++++-------
 examples/TTSwithVerification/cleanup_vllm.sh  |  26 +
 .../TTSwithVerification/run_experiments.py    | 164 ++++++
 .../start_vllm_multiprocess.sh                |  98 ++++
 6 files changed, 676 insertions(+), 174 deletions(-)
 create mode 100644 examples/TTSwithVerification/MULTIPROCESS_README.md
 create mode 100755 examples/TTSwithVerification/cleanup_vllm.sh
 create mode 100644 examples/TTSwithVerification/run_experiments.py
 create mode 100755 examples/TTSwithVerification/start_vllm_multiprocess.sh

diff --git a/.gitignore b/.gitignore
index b7faf403..d7b37631 100644
--- a/.gitignore
+++ b/.gitignore
@@ -198,6 +198,8 @@ cython_debug/
 #  Cursor is an AI-powered code editor. `.cursorignore` specifies files/directories to
 #  exclude from AI features like autocomplete and code analysis. Recommended for sensitive data
 #  refer to https://docs.cursor.com/context/ignore-files
+.*/Outputs_TTS/
+Outputs_TTS/
 .cursorignore
 .cursorindexingignore
 
diff --git a/examples/TTSwithVerification/MULTIPROCESS_README.md b/examples/TTSwithVerification/MULTIPROCESS_README.md
new file mode 100644
index 00000000..4a64612d
--- /dev/null
+++ b/examples/TTSwithVerification/MULTIPROCESS_README.md
@@ -0,0 +1,67 @@
+# Multi-Process vLLM Setup for Best-of-K Baseline
+
+This directory contains scripts and code for running the best-of-K baseline with multi-process vLLM serving.
+
+## Setup
+
+### 1. Start vLLM with 4 processes (2 GPUs each)
+
+```bash
+bash start_vllm_multiprocess.sh
+```
+
+This launches 4 vLLM OpenAI-compatible API servers:
+- **Process 1**: GPUs 0-1, Port 8000
+- **Process 2**: GPUs 2-3, Port 8001  
+- **Process 3**: GPUs 4-5, Port 8002
+- **Process 4**: GPUs 6-7, Port 8003
+
+Each process uses `tensor-parallel-size 2` for distributed inference.
+
+### 2. Run the baseline
+
+In a separate terminal:
+
+```bash
+# Test with 1 example
+python bestofk_baseline.py --task game24 --num_examples 1 --k 4 --use_critic
+
+# Run on maze dataset
+python bestofk_baseline.py --task maze --num_examples 10 --k 4
+
+# Run on spatialmap dataset
+python bestofk_baseline.py --task spatialmap --num_examples 5 --k 4
+```
+
+Or use the test script:
+```bash
+bash run_multiprocess_test.sh game24 5
+```
+
+## Load Balancing
+
+- Requests are distributed **round-robin** across the 4 vLLM instances
+- Each generation request goes to the next available port (8000 → 8001 → 8002 → 8003 → 8000 ...)
+- Critic evaluation requests use separate round-robin tracking (independent counter)
+- This ensures even load distribution across all 4 GPU pairs
+
+## Stopping vLLM
+
+```bash
+pkill -9 -f "vllm.entrypoints.openai.api_server"
+```
+
+## Configuration
+
+Edit `start_vllm_multiprocess.sh` to change:
+- `MODEL`: Model name (default: `Qwen/QwQ-32B`)
+- `MAX_TOKENS`: Maximum sequence length (default: 8192)
+- `GPU_MEMORY`: GPU memory utilization (default: 0.4)
+- `TENSOR_PARALLEL`: Must be ≤ 2 for this 8-GPU setup
+
+## Benefits
+
+- **Better throughput**: 4 independent processes handle requests in parallel
+- **Fault tolerance**: If one process crashes, others continue
+- **GPU utilization**: Balanced load across all 8 GPUs (2 GPUs per process)
+- **Reduced latency**: Each process has dedicated GPU resources
diff --git a/examples/TTSwithVerification/bestofk_baseline.py b/examples/TTSwithVerification/bestofk_baseline.py
index 0a1a0c18..9b52206d 100644
--- a/examples/TTSwithVerification/bestofk_baseline.py
+++ b/examples/TTSwithVerification/bestofk_baseline.py
@@ -4,10 +4,14 @@
 import logging
 import os
 import re
+import sys
+from contextlib import contextmanager
 from dataclasses import dataclass
-from typing import List, Optional
+from typing import Dict, List, Optional
 
 import numpy as np
+import pandas as pd
+import aiohttp
 from datasets import load_dataset
 from tqdm import tqdm
 from transformers import AutoTokenizer
@@ -15,12 +19,30 @@
 from interwhen import stream_completion
 
 # ============== MODEL CONFIGURATION ==============
-MAIN_MODEL = "Qwen/Qwen3-30B-A3B-Thinking-2507"
-# =================================================
+MAIN_MODEL = "Qwen/QwQ-32B"
+# Multi-process vLLM configuration
+VLLM_PORTS = [8000, 8001, 8002, 8003]  # 4 instances with tensor-parallel-size 2 each
+REQUEST_COUNTER = {"main": 0, "critic": 0}  # Track request count for round-robin load balancing
+
 
 logger = logging.getLogger(__name__)
 
 
+@contextmanager
+def suppress_output():
+    """Context manager to suppress stdout and stderr."""
+    with open(os.devnull, 'w') as devnull:
+        old_stdout = sys.stdout
+        old_stderr = sys.stderr
+        sys.stdout = devnull
+        sys.stderr = devnull
+        try:
+            yield
+        finally:
+            sys.stdout = old_stdout
+            sys.stderr = old_stderr
+
+
 @dataclass
 class SampleResult:
     output: str
@@ -37,15 +59,27 @@ def get_model_short_name(model_name: str) -> str:
     return short_name.replace(" ", "_").replace(":", "-")
 
 
-def get_output_dirs(task: str, main_model: str, base_dir: str = "../../b-pchanda/Outputs_TTS/BestOfKResults"):
+def get_next_port(server_type: str = "main") -> int:
+    """Get next vLLM port in round-robin fashion."""
+    global REQUEST_COUNTER
+    port = VLLM_PORTS[REQUEST_COUNTER[server_type] % len(VLLM_PORTS)]
+    REQUEST_COUNTER[server_type] += 1
+    return port
+
+
+def get_output_dirs(task: str, main_model: str, use_critic: bool, critic_early_stop: bool, base_dir: str = "../../b-pchanda/Outputs_TTS/BestOfKResults"):
     model_short_name = get_model_short_name(main_model)
-    output_base = os.path.join(base_dir, task, model_short_name)
+    critic_status = "on" if use_critic else "off"
+    earlystop_status = "on" if critic_early_stop else "off"
+    output_base = os.path.join(base_dir, task, model_short_name, f"critic_{critic_status}", f"earlystop_{earlystop_status}")
     dirs = {
         "base": output_base,
         "reasoning": os.path.join(output_base, "Reasoning_output"),
+        "critic": os.path.join(output_base, "Critic_output") if use_critic else None,
     }
     for dir_path in dirs.values():
-        os.makedirs(dir_path, exist_ok=True)
+        if dir_path:
+            os.makedirs(dir_path, exist_ok=True)
     return dirs
 
 
@@ -59,7 +93,7 @@ def init_llm_server(model_name, max_tokens=32768, port=8000, temperature=0.6, se
         "min_p": 0.0,
         "do_sample": True,
         "temperature": temperature,
-        "stream": True,
+        "stream": False,
         "logprobs": 20,
         "use_beam_search": False,
         "prompt_cache": True,
@@ -70,8 +104,16 @@ def init_llm_server(model_name, max_tokens=32768, port=8000, temperature=0.6, se
 
 
 def count_tokens(text: str, tokenizer) -> int:
-    tokens = tokenizer.encode(text, add_special_tokens=False)
-    return len(tokens)
+    """Count tokens in text, with fallback to character count."""
+    try:
+        if not text or len(text.strip()) == 0:
+            return 0
+        tokens = tokenizer.encode(text, add_special_tokens=False)
+        return len(tokens)
+    except Exception as e:
+        logger.warning(f"Tokenization failed: {e}, using character count estimate")
+        # Rough estimate: ~4 characters per token
+        return max(1, len(text) // 4)
 
 
 def save_outputs(idx: int, outputs: List[SampleResult], best_idx: int, output_dir: str):
@@ -92,7 +134,7 @@ def save_outputs(idx: int, outputs: List[SampleResult], best_idx: int, output_di
             f.write("\n")
             f.write(result.output)
             f.write("\n")
-    logger.info(f"Saved outputs to {filepath}")
+    # logger.info(f"Saved outputs to {filepath}")
 
 
 # --------------------- Game24 helpers ---------------------
@@ -211,14 +253,30 @@ def build_spatialmap_prompt(example):
 
 
 def extract_solution_mcq(text):
-    matches = re.findall(r"\\boxed\{([^}]*)\}", text)
-    if not matches:
-        return None
-    expr = matches[-1].strip()
-    choice_match = re.search(r"\b([ABCD])\b", expr, flags=re.IGNORECASE)
-    if not choice_match:
-        return None
-    return choice_match.group(1).upper()
+    """Extract MCQ solution from model output."""
+    # Try multiple boxed patterns
+    patterns = [
+        r"\\boxed\{([^}]*)\}",  # \boxed{...}
+        r"boxed\{([^}]*)\}",     # boxed{...} without escape
+        r"\*\*([A-D])\*\*",      # **A** format
+        r"answer[:\s]*([A-D])",  # answer: A format
+        r"(?:^|\n)([A-D])(?:\s|$|\.)",  # Standalone letter
+    ]
+    
+    for pattern in patterns:
+        matches = re.findall(pattern, text, re.IGNORECASE)
+        if matches:
+            expr = matches[-1].strip()
+            choice_match = re.search(r"\b([ABCD])\b", expr, flags=re.IGNORECASE)
+            if choice_match:
+                return choice_match.group(1).upper()
+    
+    # Last resort: look for any standalone A, B, C, or D
+    standalone = re.findall(r"\b([ABCD])\b", text)
+    if standalone:
+        return standalone[-1].upper()
+    
+    return None
 
 
 def extract_options_from_prompt(prompt_text, target_options):
@@ -269,7 +327,7 @@ def load_dataset_for_task(task):
     if task == "game24":
         return load_dataset("nlile/24-game", split="train")
     if task == "maze":
-        return load_dataset("microsoft/VISION_LANGUAGE", "maze", split="val")
+        return load_dataset("microsoft/VISION_LANGUAGE", "maze_text_only", split="val")
     if task == "spatialmap":
         return load_dataset("microsoft/VISION_LANGUAGE", "spatial_map_text_only", split="val")
     raise ValueError(f"Unsupported task: {task}")
@@ -295,25 +353,75 @@ def resolve_indices(task, dataset_len, args):
     return range(start, end)
 
 
-async def run_k_samples_async(prompt, llm_server, k, seed):
-    """Parallelized version - runs all k samples concurrently."""
-    tasks = []
+def batch_generate_samples(prompt, llm_server, k, seed, quiet=True):
+    """Generate k samples using vLLM batch processing via API across multiple instances."""
+    payload_template = llm_server["payload"].copy()
+    headers = llm_server["headers"]
+    
+    # Create k requests with different seeds
+    batch_payloads = []
     for i in range(k):
-        llm_server["payload"]["seed"] = seed + i
-        tasks.append(stream_completion(
-            prompt,
-            llm_server=llm_server,
-            monitors=(),
-            add_delay=False,
-            termination_requires_validation=False,
-            async_execution=True,
-        ))
-    return await asyncio.gather(*tasks)
+        payload = payload_template.copy()
+        payload["prompt"] = prompt
+        payload["seed"] = seed + i
+        batch_payloads.append(payload)
+    
+    # Send requests to vLLM instances in parallel (true concurrency)
+    async def _fetch_one(session, sem, idx, url, payload):
+        async with sem:
+            try:
+                async with session.post(url, json=payload, headers=headers, timeout=300) as resp:
+                    text = await resp.text()
+                    if resp.status >= 400:
+                        logger.warning(f"HTTP error for seed {seed + idx} on {url}: {resp.status} - {text[:200]}")
+                        return idx, ""
+                    try:
+                        result = json.loads(text)
+                    except json.JSONDecodeError:
+                        logger.warning(f"Invalid JSON for seed {seed + idx} on {url}")
+                        return idx, ""
+            except Exception as e:
+                logger.warning(f"Batch generation failed for seed {seed + idx} on {url}: {e}")
+                return idx, ""
+
+            if "choices" in result and len(result["choices"]) > 0:
+                choice = result["choices"][0]
+                if isinstance(choice, dict):
+                    output_text = choice.get("text") or choice.get("message", {}).get("content", "")
+                else:
+                    output_text = str(choice)
+                if output_text and len(output_text.strip()) > 0:
+                    return idx, output_text
+                logger.warning(f"Empty output for seed {seed + idx} on {url}")
+                return idx, ""
+
+            logger.warning(f"No choices in response for seed {seed + idx} on {url}: {result.keys() if isinstance(result, dict) else type(result)}")
+            return idx, ""
+
+    async def _run_parallel():
+        sem = asyncio.Semaphore(len(VLLM_PORTS))
+        async with aiohttp.ClientSession() as session:
+            tasks = []
+            for i, payload in enumerate(batch_payloads):
+                port = get_next_port(server_type="main")
+                url = f"http://localhost:{port}/v1/completions"
+                tasks.append(asyncio.create_task(_fetch_one(session, sem, i, url, payload)))
+            results = await asyncio.gather(*tasks)
+            return results
+
+    if quiet:
+        with suppress_output():
+            results = asyncio.run(_run_parallel())
+    else:
+        results = asyncio.run(_run_parallel())
 
+    outputs = [""] * k
+    for idx, output_text in results:
+        outputs[idx] = output_text
+        if output_text and not quiet:
+            print(f"[Generated sample {idx}] {len(output_text)} chars, {len(output_text.split())} words")
 
-def run_k_samples(prompt, llm_server, k, seed):
-    """Wrapper to run parallelized k samples."""
-    return asyncio.run(run_k_samples_async(prompt, llm_server, k, seed))
+    return outputs
 
 
 # --------------------- Critic model helpers ---------------------
@@ -364,43 +472,86 @@ def build_mcq_critic_prompt(task, task_description, reasoning_output):
 """
 
 
-async def evaluate_with_critic(output_text, task, example, critic_llm_server, tokenizer, nums=None):
-    """Use critic model to evaluate correctness of output and extract reasoning feedback."""
-    try:
-        if task == "game24":
-            critic_prompt = build_game24_critic_prompt(nums, output_text)
-        else:
-            if task == "maze":
-                _, task_desc = build_maze_prompt(example)
+def batch_evaluate_with_critic(outputs_df, task, example, critic_llm_server, tokenizer, nums=None, quiet=True):
+    """Batch evaluate outputs using vLLM API across multiple instances. Outputs_df should have columns: 'output', 'seed_idx'"""
+    payload_template = critic_llm_server["payload"].copy()
+    headers = critic_llm_server["headers"]
+
+    async def _fetch_one(session, sem, idx, url, payload):
+        async with sem:
+            try:
+                async with session.post(url, json=payload, headers=headers, timeout=300) as resp:
+                    text = await resp.text()
+                    if resp.status >= 400:
+                        logger.warning(f"HTTP error for critic sample {idx} on {url}: {resp.status} - {text[:200]}")
+                        return idx, "", False
+                    try:
+                        result = json.loads(text)
+                    except json.JSONDecodeError:
+                        logger.warning(f"Invalid JSON for critic sample {idx} on {url}")
+                        return idx, "", False
+            except Exception as e:
+                logger.warning(f"Critic evaluation failed for sample {idx} on {url}: {e}")
+                return idx, "", False
+
+            if "choices" in result and len(result["choices"]) > 0:
+                choice = result["choices"][0]
+                critic_output = choice.get("text") or choice.get("message", {}).get("content", "")
             else:
-                _, task_desc = build_spatialmap_prompt(example)
-            critic_prompt = build_mcq_critic_prompt(task, task_desc, output_text)
-        
-        critic_system = "You are a strict academic verifier."
-        full_prompt = f"<|im_start|>system\n{critic_system}<|im_end|>\n<|im_start|>user\n{critic_prompt}<|im_end|>\n<|im_start|>assistant\n"
-        
-        critic_output = await stream_completion(
-            full_prompt,
-            llm_server=critic_llm_server,
-            monitors=(),
-            add_delay=False,
-            termination_requires_validation=False,
-            async_execution=True,
-        )
-        
-        is_correct = "CORRECT" in critic_output.upper()
-        
-        # Extract reasoning from verdict and reasoning format
-        reasoning = ""
-        if "REASONING:" in critic_output:
-            reasoning = critic_output.split("REASONING:", 1)[1].strip()
-        elif "VERDICT:" not in critic_output:
-            reasoning = critic_output
-        
-        return is_correct, reasoning
-    except Exception as e:
-        logger.warning(f"Critic evaluation failed: {e}")
-        return False, ""
+                critic_output = ""
+
+            is_correct = "CORRECT" in critic_output.upper()
+            reasoning = ""
+            if "REASONING:" in critic_output:
+                reasoning = critic_output.split("REASONING:", 1)[1].strip()
+            elif "VERDICT:" not in critic_output:
+                reasoning = critic_output
+
+            return idx, reasoning, is_correct
+
+    async def _run_parallel():
+        sem = asyncio.Semaphore(len(VLLM_PORTS))
+        async with aiohttp.ClientSession() as session:
+            tasks = []
+            for idx, row in outputs_df.iterrows():
+                output_text = row["output"]
+                if task == "game24":
+                    critic_prompt = build_game24_critic_prompt(nums, output_text)
+                else:
+                    if task == "maze":
+                        _, task_desc = build_maze_prompt(example)
+                    else:
+                        _, task_desc = build_spatialmap_prompt(example)
+                    critic_prompt = build_mcq_critic_prompt(task, task_desc, output_text)
+
+                critic_system = "You are a strict academic verifier."
+                full_prompt = f"<|im_start|>system\n{critic_system}<|im_end|>\n<|im_start|>user\n{critic_prompt}<|im_end|>\n<|im_start|>assistant\n"
+
+                payload = payload_template.copy()
+                payload["prompt"] = full_prompt
+                payload["seed"] = row.get("critic_seed", idx)
+
+                port = get_next_port(server_type="critic")
+                url = f"http://localhost:{port}/v1/completions"
+                tasks.append(asyncio.create_task(_fetch_one(session, sem, idx, url, payload)))
+
+            return await asyncio.gather(*tasks)
+
+    if quiet:
+        with suppress_output():
+            results = asyncio.run(_run_parallel())
+    else:
+        results = asyncio.run(_run_parallel())
+
+    rows = []
+    for sample_idx, reasoning, is_correct in results:
+        rows.append({
+            "sample_idx": sample_idx,
+            "critic_correct": is_correct,
+            "critic_feedback": reasoning,
+        })
+
+    return pd.DataFrame(rows)
 
 
 def run_k_samples_with_critic(
@@ -415,101 +566,84 @@ def run_k_samples_with_critic(
     eval_fn,
     nums=None,
     early_stop=False,
+    quiet=True,
 ):
-    """Run up to K samples, evaluate with critic, and score with ground truth."""
+    """Run k samples with critic evaluation using vLLM batching."""
+    # Generate k samples
+    outputs = batch_generate_samples(prompt, llm_server, k, seed, quiet=quiet)
+    
+    # Create dataframe with outputs
+    df_samples = pd.DataFrame({
+        "sample_idx": range(k),
+        "output": outputs,
+        "seed": [seed + i for i in range(k)],
+    })
+    
+    # If early stop mode, stop at first critic-correct
     if early_stop:
-        # Sequential execution for early stopping
-        return _run_k_samples_with_critic_sequential(
-            prompt, llm_server, critic_llm_server, k, seed, task, example, tokenizer, eval_fn, nums
-        )
+        sample_results = []
+        for idx, row in df_samples.iterrows():
+            output = row["output"]
+            
+            # Evaluate with critic
+            df_critic = batch_evaluate_with_critic(
+                pd.DataFrame([{"output": output, "seed_idx": idx}]),
+                task, example, critic_llm_server, tokenizer, nums=nums, quiet=quiet
+            )
+            critic_correct = df_critic.iloc[0]["critic_correct"] if len(df_critic) > 0 else False
+            critic_feedback = df_critic.iloc[0]["critic_feedback"] if len(df_critic) > 0 else ""
+            
+            # Evaluate with ground truth
+            is_correct, extracted, message = eval_fn(output)
+            token_count = count_tokens(output, tokenizer)
+            
+            sample_results.append(SampleResult(
+                output=output,
+                correct=is_correct,
+                extracted=extracted,
+                message=f"Critic verdict: {'CORRECT' if critic_correct else 'INCORRECT'} | {message}",
+                tokens=token_count,
+                critic_correct=critic_correct,
+                critic_feedback=critic_feedback,
+            ))
+            
+            if critic_correct:
+                break
+        
+        return sample_results
     else:
-        # Parallelized execution when not using early stopping
-        return asyncio.run(_run_k_samples_with_critic_parallel(
-            prompt, llm_server, critic_llm_server, k, seed, task, example, tokenizer, eval_fn, nums
-        ))
+        # Batch critic evaluation
+        df_critic = batch_evaluate_with_critic(
+            df_samples, task, example, critic_llm_server, tokenizer, nums=nums, quiet=quiet
+        )
+        
+        # Merge critic results
+        df_samples = df_samples.merge(df_critic, left_index=True, right_on="sample_idx", how="left")
+        
+        # Process all results
+        sample_results = []
+        for idx, row in df_samples.iterrows():
+            output = row["output"]
+            critic_correct = row.get("critic_correct", False)
+            critic_feedback = row.get("critic_feedback", "")
+            
+            is_correct, extracted, message = eval_fn(output)
+            token_count = count_tokens(output, tokenizer)
+            
+            sample_results.append(SampleResult(
+                output=output,
+                correct=is_correct,
+                extracted=extracted,
+                message=f"Critic verdict: {'CORRECT' if critic_correct else 'INCORRECT'} | {message}",
+                tokens=token_count,
+                critic_correct=critic_correct,
+                critic_feedback=critic_feedback,
+            ))
+        
+        return sample_results
+
 
 
-def _run_k_samples_with_critic_sequential(
-    prompt, llm_server, critic_llm_server, k, seed, task, example, tokenizer, eval_fn, nums=None
-):
-    """Sequential version - required for early stopping."""
-    sample_results = []
-    for i in range(k):
-        llm_server["payload"]["seed"] = seed + i
-        output = asyncio.run(stream_completion(
-            prompt,
-            llm_server=llm_server,
-            monitors=(),
-            add_delay=False,
-            termination_requires_validation=False,
-            async_execution=True,
-        ))
-
-        critic_correct, critic_feedback = asyncio.run(evaluate_with_critic(
-            output, task, example, critic_llm_server, tokenizer, nums=nums
-        ))
-        is_correct, extracted, message = eval_fn(output)
-        token_count = count_tokens(output, tokenizer)
-
-        sample_results.append(SampleResult(
-            output=output,
-            correct=is_correct,
-            extracted=extracted,
-            message=f"Critic verdict: {'CORRECT' if critic_correct else 'INCORRECT'} | {message}",
-            tokens=token_count,
-            critic_correct=critic_correct,
-            critic_feedback=critic_feedback,
-        ))
-
-        if critic_correct:
-            break
-
-    return sample_results
-
-
-async def _run_k_samples_with_critic_parallel(
-    prompt, llm_server, critic_llm_server, k, seed, task, example, tokenizer, eval_fn, nums=None
-):
-    """Parallelized version - runs all k samples concurrently and evaluates with critic."""
-    # Step 1: Generate all outputs in parallel
-    output_tasks = []
-    for i in range(k):
-        llm_server["payload"]["seed"] = seed + i
-        output_tasks.append(stream_completion(
-            prompt,
-            llm_server=llm_server,
-            monitors=(),
-            add_delay=False,
-            termination_requires_validation=False,
-            async_execution=True,
-        ))
-    outputs = await asyncio.gather(*output_tasks)
-
-    # Step 2: Evaluate all outputs in parallel
-    evaluation_tasks = []
-    for output in outputs:
-        evaluation_tasks.append(evaluate_with_critic(
-            output, task, example, critic_llm_server, tokenizer, nums=nums
-        ))
-    critic_evaluations = await asyncio.gather(*evaluation_tasks)
-
-    # Step 3: Compile results
-    sample_results = []
-    for output, (critic_correct, critic_feedback) in zip(outputs, critic_evaluations):
-        is_correct, extracted, message = eval_fn(output)
-        token_count = count_tokens(output, tokenizer)
-
-        sample_results.append(SampleResult(
-            output=output,
-            correct=is_correct,
-            extracted=extracted,
-            message=f"Critic verdict: {'CORRECT' if critic_correct else 'INCORRECT'} | {message}",
-            tokens=token_count,
-            critic_correct=critic_correct,
-            critic_feedback=critic_feedback,
-        ))
-
-    return sample_results
 
 
 if __name__ == "__main__":
@@ -538,11 +672,16 @@ async def _run_k_samples_with_critic_parallel(
     parser.add_argument("--debug", "-d", action="store_true", help="Enable debug logging")
     args = parser.parse_args()
 
-    log_level = logging.DEBUG if args.debug else logging.INFO
+    log_level = logging.DEBUG if args.debug else logging.ERROR
     logging.basicConfig(level=log_level, format="%(message)s")
 
+    quiet_mode = not args.debug
 
-    dataset = load_dataset_for_task(args.task)
+    if quiet_mode:
+        with suppress_output():
+            dataset = load_dataset_for_task(args.task)
+    else:
+        dataset = load_dataset_for_task(args.task)
     indices = resolve_indices(args.task, len(dataset), args)
 
     llm_server = init_llm_server(
@@ -562,13 +701,17 @@ async def _run_k_samples_with_critic_parallel(
             temperature=0.2,
             seed=args.seed,
         )
-        logger.info(f"Using critic model: {args.critic_model} on port {args.critic_port}")
+        # logger.info(f"Using critic model: {args.critic_model} on port {args.critic_port}")
 
-    logger.info(f"Loading tokenizer for {args.main_model}...")
-    tokenizer = AutoTokenizer.from_pretrained(args.main_model, trust_remote_code=True)
-    logger.info("Tokenizer loaded successfully.")
+    # logger.info(f"Loading tokenizer for {args.main_model}...")
+    if quiet_mode:
+        with suppress_output():
+            tokenizer = AutoTokenizer.from_pretrained(args.main_model, trust_remote_code=True)
+    else:
+        tokenizer = AutoTokenizer.from_pretrained(args.main_model, trust_remote_code=True)
+    # logger.info("Tokenizer loaded successfully.")
 
-    output_dirs = get_output_dirs(args.task, args.main_model)
+    output_dirs = get_output_dirs(args.task, args.main_model, args.use_critic, args.critic_early_stop)
 
     total_examples = 0
     total_correct = 0
@@ -601,16 +744,18 @@ async def _run_k_samples_with_critic_parallel(
             options = extract_options_from_prompt(user_prompt, target_options)
             eval_fn = lambda output: evaluate_mcq_answer(output, options, gt)
 
-        logger.info(f"---- Example {idx} ----")
+        #logger.info(f"---- Example {idx} ----")
+        
+        quiet_mode = not args.debug
         
         if args.use_critic:
             sample_results = run_k_samples_with_critic(
                 prompt, llm_server, critic_llm_server, args.k, args.seed,
                 args.task, example, tokenizer, eval_fn, nums=(nums if args.task == "game24" else None),
-                early_stop=args.critic_early_stop
+                early_stop=args.critic_early_stop, quiet=quiet_mode
             )
         else:
-            outputs = run_k_samples(prompt, llm_server, args.k, args.seed)
+            outputs = batch_generate_samples(prompt, llm_server, args.k, args.seed, quiet=quiet_mode)
             sample_results = []
             for output in outputs:
                 is_correct, extracted, message = eval_fn(output)
@@ -662,8 +807,8 @@ async def _run_k_samples_with_critic_parallel(
             "options": options,
         })
 
-        logger.info(f"Best sample: {best_idx} | Correct in K: {any_correct}")
-        logger.info(f"Best message: {best_result.message}")
+        #logger.info(f"Best sample: {best_idx} | Correct in K: {any_correct}")
+        #logger.info(f"Best message: {best_result.message}")
 
     accuracy = total_correct / total_examples if total_examples else 0
     avg_best_tokens = total_tokens / total_examples if total_examples else 0
@@ -698,4 +843,4 @@ async def _run_k_samples_with_critic_parallel(
     summary_path = os.path.join(output_dirs["base"], "summary.json")
     with open(summary_path, "w", encoding="utf-8") as f:
         json.dump(summary, f, indent=2)
-    logger.info(f"Saved summary to {summary_path}")
+    # logger.info(f"Saved summary to {summary_path}")
diff --git a/examples/TTSwithVerification/cleanup_vllm.sh b/examples/TTSwithVerification/cleanup_vllm.sh
new file mode 100755
index 00000000..f552ec11
--- /dev/null
+++ b/examples/TTSwithVerification/cleanup_vllm.sh
@@ -0,0 +1,26 @@
+#!/bin/bash
+
+# Cleanup script to kill all vLLM processes and Python instances
+
+echo "Stopping all vLLM processes..."
+pkill -9 -f "vllm.entrypoints.openai.api_server"
+
+echo "Stopping Python processes..."
+pkill -9 -f "bestofk_baseline.py"
+
+sleep 2
+
+echo "Verifying all processes stopped..."
+if pgrep -f "vllm.entrypoints.openai.api_server" > /dev/null; then
+    echo "WARNING: Some vLLM processes still running"
+else
+    echo "✓ All vLLM processes stopped"
+fi
+
+if pgrep -f "bestofk_baseline.py" > /dev/null; then
+    echo "WARNING: Some Python processes still running"
+else
+    echo "✓ All Python processes stopped"
+fi
+
+echo "Cleanup complete"
diff --git a/examples/TTSwithVerification/run_experiments.py b/examples/TTSwithVerification/run_experiments.py
new file mode 100644
index 00000000..a52952b0
--- /dev/null
+++ b/examples/TTSwithVerification/run_experiments.py
@@ -0,0 +1,164 @@
+#!/usr/bin/env python3
+"""
+Job scheduler for running bestofk_baseline.py experiments sequentially.
+"""
+import subprocess
+import sys
+import time
+from datetime import datetime
+from pathlib import Path
+
+# Base command
+BASE_CMD = "python /data/b-pchanda/interwhen/examples/TTSwithVerification/bestofk_baseline.py"
+
+# Define your experiment configurations
+EXPERIMENTS = [
+    # Maze experiments
+    {
+        "name": "maze_k4_critic",
+        "args": "--task maze --k 4 --use_critic"
+    },
+    {
+        "name": "maze_k4_critic_earlystop",
+        "args": "--task maze --k 4 --use_critic --critic_early_stop"
+    },
+    {
+        "name": "maze_k4_no_critic",
+        "args": "--task maze --k 4"
+    },
+    
+    # Game24 experiments
+    {
+        "name": "game24_k4_critic",
+        "args": "--task game24 --k 4 --use_critic"
+    },
+    {
+        "name": "game24_k4_critic_earlystop",
+        "args": "--task game24 --k 4 --use_critic --critic_early_stop"
+    },
+    {
+        "name": "game24_k4_no_critic",
+        "args": "--task game24 --k 4"
+    },
+    
+    # Spatialmap experiments
+    {
+        "name": "spatialmap_k4_critic",
+        "args": "--task spatialmap --k 4 --use_critic"
+    },
+    {
+        "name": "spatialmap_k4_critic_earlystop",
+        "args": "--task spatialmap --k 4 --use_critic --critic_early_stop"
+    },
+    {
+        "name": "spatialmap_k4_no_critic",
+        "args": "--task spatialmap --k 4"
+    },
+]
+
+
+def run_experiment(exp_config, exp_num, total_exps):
+    """Run a single experiment."""
+    name = exp_config["name"]
+    args = exp_config["args"]
+    
+    print("\n" + "="*80)
+    print(f"Experiment [{exp_num}/{total_exps}]: {name}")
+    print(f"Command: {BASE_CMD} {args}")
+    print("="*80)
+    
+    start_time = time.time()
+    start_ts = datetime.now().strftime("%Y-%m-%d %H:%M:%S")
+    
+    try:
+        # Run the command
+        result = subprocess.run(
+            f"{BASE_CMD} {args}",
+            shell=True,
+            capture_output=False,  # Show output in real-time
+            text=True
+        )
+        
+        elapsed = time.time() - start_time
+        end_ts = datetime.now().strftime("%Y-%m-%d %H:%M:%S")
+        
+        if result.returncode == 0:
+            print(f"\n✓ Experiment '{name}' completed successfully")
+            print(f"  Started:  {start_ts}")
+            print(f"  Finished: {end_ts}")
+            print(f"  Duration: {elapsed:.1f}s ({elapsed/60:.1f} min)")
+            return True, elapsed
+        else:
+            print(f"\n✗ Experiment '{name}' failed with exit code {result.returncode}")
+            print(f"  Duration: {elapsed:.1f}s")
+            return False, elapsed
+            
+    except KeyboardInterrupt:
+        print(f"\n\n⚠ Experiment '{name}' interrupted by user")
+        raise
+    except Exception as e:
+        elapsed = time.time() - start_time
+        print(f"\n✗ Experiment '{name}' failed with exception: {e}")
+        print(f"  Duration: {elapsed:.1f}s")
+        return False, elapsed
+
+
+def main():
+    """Run all experiments sequentially."""
+    print("="*80)
+    print("JOB SCHEDULER - Running experiments sequentially")
+    print("="*80)
+    print(f"Total experiments: {len(EXPERIMENTS)}")
+    print(f"Started at: {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}")
+    
+    results = []
+    total_start = time.time()
+    
+    try:
+        for i, exp in enumerate(EXPERIMENTS, 1):
+            success, duration = run_experiment(exp, i, len(EXPERIMENTS))
+            results.append({
+                "name": exp["name"],
+                "success": success,
+                "duration": duration
+            })
+            
+            # Brief pause between experiments
+            if i < len(EXPERIMENTS):
+                print("\nWaiting 5 seconds before next experiment...")
+                time.sleep(5)
+    
+    except KeyboardInterrupt:
+        print("\n\n⚠ Job scheduler interrupted by user")
+        
+    finally:
+        # Print summary
+        total_elapsed = time.time() - total_start
+        print("\n" + "="*80)
+        print("SUMMARY")
+        print("="*80)
+        
+        successful = sum(1 for r in results if r["success"])
+        failed = len(results) - successful
+        
+        print(f"\nCompleted: {len(results)}/{len(EXPERIMENTS)} experiments")
+        print(f"Successful: {successful}")
+        print(f"Failed: {failed}")
+        print(f"\nTotal time: {total_elapsed:.1f}s ({total_elapsed/60:.1f} min, {total_elapsed/3600:.2f} hrs)")
+        
+        print("\nDetailed results:")
+        for i, r in enumerate(results, 1):
+            status = "✓" if r["success"] else "✗"
+            print(f"  {i}. {status} {r['name']:40s} - {r['duration']:.1f}s ({r['duration']/60:.1f} min)")
+        
+        if failed > 0:
+            print("\nFailed experiments:")
+            for i, r in enumerate(results, 1):
+                if not r["success"]:
+                    print(f"  {i}. {r['name']}")
+        
+        sys.exit(0 if failed == 0 else 1)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/TTSwithVerification/start_vllm_multiprocess.sh b/examples/TTSwithVerification/start_vllm_multiprocess.sh
new file mode 100755
index 00000000..080b58b7
--- /dev/null
+++ b/examples/TTSwithVerification/start_vllm_multiprocess.sh
@@ -0,0 +1,98 @@
+#!/bin/bash
+
+# Start 4 vLLM processes with explicit GPU assignment
+# Process 1: GPUs 0-1, Port 8000
+# Process 2: GPUs 2-3, Port 8001
+# Process 3: GPUs 4-5, Port 8002
+# Process 4: GPUs 6-7, Port 8003
+
+MODEL="Qwen/QwQ-32B"
+GPU_MEMORY=0.4
+TENSOR_PARALLEL=2
+
+echo "Killing any existing vLLM processes..."
+pkill -9 -f "vllm.entrypoints.openai.api_server"
+sleep 2
+
+echo "Starting 4 vLLM processes..."
+
+# Process 1 - GPUs 0,1
+(
+    export CUDA_VISIBLE_DEVICES=0,1
+    python -m vllm.entrypoints.openai.api_server \
+        --model $MODEL \
+        --port 8000 \
+        --tensor-parallel-size $TENSOR_PARALLEL \
+        --gpu-memory-utilization $GPU_MEMORY \
+        --disable-log-requests \
+        > /tmp/vllm_8000.log 2>&1
+) &
+PID1=$!
+echo "Started Process 1 (GPUs 0-1, Port 8000) - PID: $PID1"
+
+sleep 5
+
+# Process 2 - GPUs 2,3
+(
+    export CUDA_VISIBLE_DEVICES=2,3
+    python -m vllm.entrypoints.openai.api_server \
+        --model $MODEL \
+        --port 8001 \
+        --tensor-parallel-size $TENSOR_PARALLEL \
+        --gpu-memory-utilization $GPU_MEMORY \
+        --disable-log-requests \
+        > /tmp/vllm_8001.log 2>&1
+) &
+PID2=$!
+echo "Started Process 2 (GPUs 2-3, Port 8001) - PID: $PID2"
+
+sleep 5
+
+# Process 3 - GPUs 4,5
+(
+    export CUDA_VISIBLE_DEVICES=4,5
+    python -m vllm.entrypoints.openai.api_server \
+        --model $MODEL \
+        --port 8002 \
+        --tensor-parallel-size $TENSOR_PARALLEL \
+        --gpu-memory-utilization $GPU_MEMORY \
+        --disable-log-requests \
+        > /tmp/vllm_8002.log 2>&1
+) &
+PID3=$!
+echo "Started Process 3 (GPUs 4-5, Port 8002) - PID: $PID3"
+
+sleep 5
+
+# Process 4 - GPUs 6,7
+(
+    export CUDA_VISIBLE_DEVICES=6,7
+    python -m vllm.entrypoints.openai.api_server \
+        --model $MODEL \
+        --port 8003 \
+        --tensor-parallel-size $TENSOR_PARALLEL \
+        --gpu-memory-utilization $GPU_MEMORY \
+        --disable-log-requests \
+        > /tmp/vllm_8003.log 2>&1
+) &
+PID4=$!
+echo "Started Process 4 (GPUs 6-7, Port 8003) - PID: $PID4"
+
+echo ""
+echo "All 4 vLLM processes started successfully."
+echo "Process PIDs: $PID1 $PID2 $PID3 $PID4"
+echo ""
+echo "Log files:"
+echo "  /tmp/vllm_8000.log - Process 1"
+echo "  /tmp/vllm_8001.log - Process 2"
+echo "  /tmp/vllm_8002.log - Process 3"
+echo "  /tmp/vllm_8003.log - Process 4"
+echo ""
+echo "To stop all processes, run:"
+echo "  pkill -9 -f 'vllm.entrypoints.openai.api_server'"
+echo ""
+echo "Waiting for processes to initialize (this may take 60-120 seconds)..."
+echo ""
+
+# Wait for all processes
+wait $PID1 $PID2 $PID3 $PID4

From 36ca8a21bee30c02153bce610d124bdd686fd746 Mon Sep 17 00:00:00 2001
From: ashmitkx <66110457+ashmitkx@users.noreply.github.com>
Date: Tue, 3 Mar 2026 12:35:47 +0000
Subject: [PATCH 04/11] add zebralogic to bon+gentest

---
 .../TTSwithVerification/bestofk_baseline.py   |     59 +-
 interwhen/data/__init__.py                    |      0
 interwhen/data/zebralogic_ir_map.json         | 285374 +++++++++++++++
 interwhen/utils/zebralogic_helper.py          |    284 +
 4 files changed, 285716 insertions(+), 1 deletion(-)
 create mode 100644 interwhen/data/__init__.py
 create mode 100644 interwhen/data/zebralogic_ir_map.json
 create mode 100644 interwhen/utils/zebralogic_helper.py

diff --git a/examples/TTSwithVerification/bestofk_baseline.py b/examples/TTSwithVerification/bestofk_baseline.py
index 9b52206d..a168ceec 100644
--- a/examples/TTSwithVerification/bestofk_baseline.py
+++ b/examples/TTSwithVerification/bestofk_baseline.py
@@ -16,6 +16,8 @@
 from tqdm import tqdm
 from transformers import AutoTokenizer
 
+from interwhen.utils.zebralogic_helper import SYSTEM_PROMPT_VANILLA, USER_PROMPT_TEMPLATE, get_zebralogic_dataset, extract_last_json, zebra_correctness
+
 from interwhen import stream_completion
 
 # ============== MODEL CONFIGURATION ==============
@@ -307,6 +309,24 @@ def evaluate_mcq_answer(answer, options, ground_truth):
             return False, sol, f"Incorrect: expected '{gt_sol}', got '{opt_value}' (option {opt_letter})"
     return False, sol, f"Solution '{sol}' not found in options or ground truth"
 
+# --------------------- ZebraLogic helpers ---------------------
+
+def evaluate_zebralogic_answer(answer, example):
+    """Evaluate a zebralogic answer against ground truth using zebra_correctness."""
+    candidate = extract_last_json(answer)
+    if not candidate:
+        return False, None, "No valid JSON solution found"
+    correct, skipped, missing, total = zebra_correctness(example, candidate)
+    is_correct = correct == total
+    msg = f"Correct={correct}/{total}, skipped={skipped}, missing={missing}"
+    return is_correct, candidate, msg
+
+
+def build_zebralogic_prompt(example):
+    system_prompt = SYSTEM_PROMPT_VANILLA
+    user_prompt = USER_PROMPT_TEMPLATE.format(problem_text=example['puzzle_clean'])
+    return system_prompt, user_prompt
+
 
 def build_full_prompt(task, example, nums=None):
     if task == "game24":
@@ -314,6 +334,8 @@ def build_full_prompt(task, example, nums=None):
         return f"<|im_start|>user\n{prompt}<|im_end|>\n<|im_start|>assistant\n"
     if task == "maze":
         system_prompt, user_prompt = build_maze_prompt(example)
+    elif task == 'zebralogic':
+        system_prompt, user_prompt = build_zebralogic_prompt(example)
     else:
         system_prompt, user_prompt = build_spatialmap_prompt(example)
     return (
@@ -330,6 +352,8 @@ def load_dataset_for_task(task):
         return load_dataset("microsoft/VISION_LANGUAGE", "maze_text_only", split="val")
     if task == "spatialmap":
         return load_dataset("microsoft/VISION_LANGUAGE", "spatial_map_text_only", split="val")
+    if task == "zebralogic":
+        return get_zebralogic_dataset()
     raise ValueError(f"Unsupported task: {task}")
 
 
@@ -450,6 +474,30 @@ def build_game24_critic_prompt(nums, reasoning_output):
 """
 
 
+def build_zebralogic_critic_prompt(task_description, reasoning_output):
+    """Build critic prompt to evaluate ZebraLogic solution and provide reasoning."""
+    return f"""You are an expert logic puzzle verifier. Evaluate the following ZebraLogic solution.
+
+Task:
+{task_description}
+
+Student's reasoning and answer:
+{reasoning_output}
+
+Verify:
+1. Does the solution assign exactly one value per feature per house?
+2. Are all constraints/clues satisfied?
+3. Is the JSON output well-formed and complete?
+
+Respond in the following format:
+VERDICT: CORRECT or INCORRECT
+REASONING: Your detailed explanation
+
+If CORRECT, briefly explain why.
+If INCORRECT, explain what went wrong and suggest corrections.
+"""
+
+
 def build_mcq_critic_prompt(task, task_description, reasoning_output):
     """Build critic prompt to evaluate MCQ solution and provide reasoning."""
     task_name = "Maze" if task == "maze" else "Spatial Reasoning"
@@ -517,6 +565,9 @@ async def _run_parallel():
                 output_text = row["output"]
                 if task == "game24":
                     critic_prompt = build_game24_critic_prompt(nums, output_text)
+                elif task == "zebralogic":
+                    _, task_desc = build_zebralogic_prompt(example)
+                    critic_prompt = build_zebralogic_critic_prompt(task_desc, output_text)
                 else:
                     if task == "maze":
                         _, task_desc = build_maze_prompt(example)
@@ -648,7 +699,7 @@ def run_k_samples_with_critic(
 
 if __name__ == "__main__":
     parser = argparse.ArgumentParser(description="Best-of-K baseline (standard CoT) for TTSwithVerification datasets")
-    parser.add_argument("--task", type=str, required=True, choices=["game24", "maze", "spatialmap"],
+    parser.add_argument("--task", type=str, required=True, choices=["game24", "maze", "spatialmap", "zebralogic"],
                         help="Task to run")
     parser.add_argument("--k", type=int, default=4, help="Number of samples per example")
     parser.add_argument("--num_examples", "-n", type=int, default=None,
@@ -730,6 +781,12 @@ def run_k_samples_with_critic(
             prompt = build_full_prompt(args.task, example, nums=nums)
             eval_fn = lambda output: evaluate_game24_answer(output, nums)
             options = None
+        
+        elif args.task == "zebralogic":
+            prompt = build_full_prompt(args.task, example)
+            eval_fn = lambda output, ex=example: evaluate_zebralogic_answer(output, ex)
+            options = None
+        
         else:
             prompt = build_full_prompt(args.task, example)
             gt = str(example.get("ground_truth", "")).strip()
diff --git a/interwhen/data/__init__.py b/interwhen/data/__init__.py
new file mode 100644
index 00000000..e69de29b
diff --git a/interwhen/data/zebralogic_ir_map.json b/interwhen/data/zebralogic_ir_map.json
new file mode 100644
index 00000000..2558c733
--- /dev/null
+++ b/interwhen/data/zebralogic_ir_map.json
@@ -0,0 +1,285374 @@
+{
+    "lgp-test-2x2-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "holly"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "holly"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "holly"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "iris"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "iris"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "samantha"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "roses"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "milk"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "water"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "timothy"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "verytall"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "milk"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "may"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "purple"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "samantha"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "master"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "holly"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "volleyball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "supertall"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "purple"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "soup"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "samantha"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "alice"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "milk"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "german"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "milk"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "cigar",
+                            "yellow monster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "cigar",
+                            "yellow monster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "penny"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "penny"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "water"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "purple"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "master"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "purple"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "purple"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "soup"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "flower",
+                            "iris"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "german"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "blue"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "water"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "children",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "children",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "verytall"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "milk"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "iris"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "flower",
+                            "iris"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "flower",
+                            "iris"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "trade school"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "iris"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "roses"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "flower",
+                            "iris"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "flower",
+                            "iris"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "samantha"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "holly"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "roses"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "milk"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "mother",
+                            "sarah"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "iris"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "iris"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "education",
+                            "trade school"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "roses"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "nationality",
+                            "chinese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "chinese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "german"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "samantha"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "roses"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "flower",
+                            "iris"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "iris"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "water"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "children",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "water"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "water"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "iris"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "soup"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "soup"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "milk"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "education",
+                            "trade school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "mother",
+                            "sarah"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "flower",
+                            "iris"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "samantha"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "iris"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "soup"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "soup"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "water"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "children",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "timothy"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "iris"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "timothy"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "purple"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "iris"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "milk"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "penny"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "penny"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "holly"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "penny"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "soup"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "trade school"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "nationality",
+                            "chinese"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "samantha"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "supertall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "milk"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "master"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "blue"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "purple"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "water"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "blue"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "purple"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "blue"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "master"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "master"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "holly"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "water"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "blue"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "children",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "country"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "milk"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "roses"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "verytall"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "supertall"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "country"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "B": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "samantha"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "cigar",
+                            "yellow monster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "milk"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "cigar",
+                            "yellow monster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "volleyball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "volleyball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "supertall"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "timothy"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "master"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "trade school"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "education",
+                            "trade school"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "soup"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "soup"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "iris"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "mother",
+                            "sarah"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "sarah"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "holly"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "samantha"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "penny"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "purple"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "iris"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "milk"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-11": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "iris"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "holly"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "iris"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "purple"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "purple"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "sarah"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-8": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "nationality",
+                            "chinese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "water"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "penny"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "blue"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "education",
+                            "trade school"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "education",
+                            "trade school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "soup"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "soup"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-0": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x3-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-36": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "water"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "water"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "german"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "soup"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "stew"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "blueberry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "soup"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-6": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-20": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-35": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "timothy"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x6-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "birthday",
+                            "may"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "carol"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "mother",
+                            "holly"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-15": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x6-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x2-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "children",
+                            "samantha"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-16": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-24": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "soup"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "food",
+                            "pizza"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "stew"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-7": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "education",
+                            "trade school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "volleyball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "trade school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "associate"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x3-19": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "education",
+                            "master"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-9": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "bird"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x5-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-29": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "ranch"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x2-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x4-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "baseball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "supertall"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "horse"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-2x5-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "water"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "april"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "april"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x3-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "drink",
+                            "tea"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x2-32": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "master"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "hobby",
+                            "gardening"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-5": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "white"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x2-3": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-25": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x4-37": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "cigar",
+                            "dunhill"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x3-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-31": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "biography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "cherry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "birthday",
+                            "feb"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "height",
+                            "verytall"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-22": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "occupation",
+                            "artist"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "occupation",
+                            "doctor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "purple"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "color",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "red"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "green"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x2-28": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "bella"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "children",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "timothy"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "children",
+                            "meredith"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "bella"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "samantha"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "fred"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "alice"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-3x4-1": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "city"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-2": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "children",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "average"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "children",
+                            "meredith"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "children",
+                            "samantha"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "bob"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "alice"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "may"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "birthday",
+                            "mar"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "cigar",
+                            "prince"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "cigar",
+                            "yellow monster"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x5-27": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "jan"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "birthday",
+                            "may"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "chevrolet silverado"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "birthday",
+                            "april"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "may"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "children",
+                            "bella"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "children",
+                            "meredith"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "children",
+                            "fred"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "children",
+                            "fred"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "romance"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "children",
+                            "timothy"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "science fiction"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "mother",
+                            "penny"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "fred"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "meredith"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "bella"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "timothy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "children",
+                        "samantha"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "soup"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "root beer"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "food",
+                            "soup"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "verytall"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "occupation",
+                            "engineer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "roses"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "teacher"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "lime"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "food",
+                            "soup"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "nurse"
+                        ],
+                        "B": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "food",
+                            "stew"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "lawyer"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "occupation",
+                            "engineer"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "rock"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "blueberry"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "carol"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "nurse"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "country"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "soup"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "blueberry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x5-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "ford f150"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-4x6-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "ranch"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-13": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "master"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "education",
+                            "high school"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x4-12": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "food",
+                            "pizza"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "B": [
+                            "food",
+                            "pizza"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "stir fry"
+                        ],
+                        "B": [
+                            "education",
+                            "doctorate"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "high school"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "food",
+                            "stir fry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "grilled cheese"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "education",
+                            "associate"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "food",
+                            "spaghetti"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stir fry"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "stew"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "spaghetti"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "grilled cheese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "food",
+                        "pizza"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-21": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "colonial"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "lime"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "brit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "horse"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "craftsman"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "smoothie",
+                            "dragonfruit"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "victorian"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "desert"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-18": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "bookgenre",
+                            "fantasy"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "tesla model 3"
+                        ],
+                        "B": [
+                            "pet",
+                            "hamster"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "cat"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "carmodel",
+                            "honda civic"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "science fiction"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "honda civic"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "toyota camry"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "bookgenre",
+                            "romance"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "carmodel",
+                            "ford f150"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "fantasy"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "carmodel",
+                            "bmw 3 series"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "bookgenre",
+                            "mystery"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "bookgenre",
+                            "historical fiction"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "nationality",
+                            "dane"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "eric"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "fantasy"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "honda civic"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "mystery"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "bmw 3 series"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "science fiction"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "toyota camry"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "historical fiction"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "tesla model 3"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "romance"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "chevrolet silverado"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "bookgenre",
+                        "biography"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "carmodel",
+                        "ford f150"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-10": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "fish"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "height",
+                            "tall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "supertall"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "short"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "basketball"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x6-17": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "smoothie",
+                            "watermelon"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "fish"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "desert"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "smoothie",
+                            "cherry"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "vacation",
+                            "mountain"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "smoothie",
+                            "dragonfruit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "beach"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "watermelon"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "cherry"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "lime"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "dragonfruit"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "smoothie",
+                        "desert"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-38": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "arnold"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "name",
+                            "peter"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "musicgenre",
+                            "classical"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "musicgenre",
+                            "pop"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "hip hop"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "classical"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "musicgenre",
+                            "jazz"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "rock"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "hip hop"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "classical"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "pop"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "musicgenre",
+                        "jazz"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x4-33": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "short"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "pos": 6
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "nationality",
+                            "german"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "nationality",
+                            "dane"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-39": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "mar"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "birthday",
+                            "feb"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "doctor"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "occupation",
+                            "artist"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "penny"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "occupation",
+                            "teacher"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "B": [
+                            "birthday",
+                            "jan"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "holly"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "occupation",
+                            "lawyer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "birthday",
+                            "sept"
+                        ],
+                        "B": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "gray"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "feb"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "doctor"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "sept"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "lawyer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "april"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "engineer"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "jan"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "artist"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "birthday",
+                        "mar"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "occupation",
+                        "teacher"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x5-34": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "pet",
+                            "bird"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "pet",
+                            "cat"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "average"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "height",
+                            "veryshort"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "mother",
+                            "janelle"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "mother",
+                            "penny"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "hamster"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "mother",
+                            "aniya"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "pet",
+                            "dog"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "mother",
+                            "kailyn"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "bird"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "hamster"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "penny"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "holly"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "janelle"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "kailyn"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "mother",
+                        "aniya"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-5x3-14": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "color",
+                            "yellow"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "name",
+                            "arnold"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 5
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-30": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "german"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "white"
+                        ],
+                        "B": [
+                            "drink",
+                            "coffee"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "water"
+                        ],
+                        "B": [
+                            "color",
+                            "purple"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "education",
+                            "high school"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "iris"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "education",
+                            "associate"
+                        ],
+                        "B": [
+                            "color",
+                            "green"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "nationality",
+                            "chinese"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "color",
+                            "red"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "alice"
+                        ],
+                        "B": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "nationality",
+                            "brit"
+                        ],
+                        "B": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "education",
+                            "bachelor"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "color",
+                            "yellow"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "milk"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "swede"
+                        ],
+                        "B": [
+                            "education",
+                            "master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "education",
+                            "trade school"
+                        ],
+                        "B": [
+                            "nationality",
+                            "chinese"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "nationality",
+                            "german"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "nationality",
+                            "norwegian"
+                        ],
+                        "B": [
+                            "drink",
+                            "water"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "dane"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "trade school"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "brit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "associate"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "swede"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "master"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "chinese"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "bachelor"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "german"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "doctorate"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "nationality",
+                        "norwegian"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "education",
+                        "high school"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-23": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "camping"
+                        ],
+                        "B": [
+                            "hobby",
+                            "cooking"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "hobby",
+                            "photography"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "vacation",
+                            "city"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "tennis"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "swimming"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "photography"
+                        ],
+                        "B": [
+                            "drink",
+                            "tea"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "peter"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "knitting"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "drink",
+                            "boba tea"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "cat"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "vacation",
+                            "beach"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "drink",
+                            "coffee"
+                        ],
+                        "B": [
+                            "name",
+                            "alice"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "drink",
+                            "tea"
+                        ],
+                        "B": [
+                            "pet",
+                            "fish"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "drink",
+                            "milk"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "rabbit"
+                        ],
+                        "B": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "direction": "any",
+                        "dist": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "hobby",
+                            "cooking"
+                        ],
+                        "pos": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "tennis"
+                        ],
+                        "B": [
+                            "pet",
+                            "rabbit"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "pet",
+                            "dog"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "hobby",
+                            "woodworking"
+                        ],
+                        "B": [
+                            "pet",
+                            "dog"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "hobby",
+                            "painting"
+                        ],
+                        "B": [
+                            "pet",
+                            "horse"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "drink",
+                            "root beer"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "cat"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "cooking"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "boba tea"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "rabbit"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "painting"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "milk"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "fish"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "photography"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "tea"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "dog"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "woodworking"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "water"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "horse"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "knitting"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "coffee"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "pet",
+                        "bird"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "hobby",
+                        "gardening"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "drink",
+                        "root beer"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-4": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "lilies"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "auburn"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "vacation",
+                            "camping"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "auburn"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "cultural"
+                        ],
+                        "B": [
+                            "height",
+                            "supertall"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "haircolor",
+                            "gray"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "tall"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "craftsman"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "height",
+                            "veryshort"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "blonde"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "height",
+                            "verytall"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "roses"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "modern"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "city"
+                        ],
+                        "B": [
+                            "height",
+                            "short"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "housestyle",
+                            "colonial"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "brown"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "haircolor",
+                            "red"
+                        ],
+                        "B": [
+                            "flower",
+                            "lilies"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "victorian"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "B": [
+                            "housestyle",
+                            "modern"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "arnold"
+                        ],
+                        "B": [
+                            "height",
+                            "average"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "height",
+                            "tall"
+                        ],
+                        "pos": 5
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "not_place",
+                        "entity": [
+                            "flower",
+                            "tulips"
+                        ],
+                        "pos": 4
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "name",
+                            "bob"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "verytall"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cultural"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "housestyle",
+                            "mediterranean"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "red"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "height",
+                            "supertall"
+                        ],
+                        "B": [
+                            "haircolor",
+                            "black"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "vacation",
+                            "mountain"
+                        ],
+                        "B": [
+                            "vacation",
+                            "cruise"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "mountain"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "victorian"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "veryshort"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "auburn"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cruise"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "modern"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "tall"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "gray"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "cultural"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "craftsman"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "verytall"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "brown"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "beach"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "colonial"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "supertall"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "black"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "city"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "ranch"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "short"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "blonde"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "vacation",
+                        "camping"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "housestyle",
+                        "mediterranean"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "height",
+                        "average"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "haircolor",
+                        "red"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    },
+    "lgp-test-6x6-26": {
+        "clue_irs": [
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "pos": 2
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "xiaomi mi 11"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "flower",
+                            "carnations"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "purple"
+                        ],
+                        "B": [
+                            "cigar",
+                            "pall mall"
+                        ],
+                        "direction": "left",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "green"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "color",
+                            "yellow"
+                        ],
+                        "B": [
+                            "color",
+                            "blue"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "samsung galaxy s21"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "flower",
+                            "daffodils"
+                        ],
+                        "direction": "any",
+                        "dist": 3
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "prince"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "basketball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "volleyball"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "swimming"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "huawei p50"
+                        ],
+                        "B": [
+                            "color",
+                            "white"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "oneplus 9"
+                        ],
+                        "B": [
+                            "flower",
+                            "roses"
+                        ],
+                        "direction": "any",
+                        "dist": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "iris"
+                        ],
+                        "B": [
+                            "name",
+                            "eric"
+                        ],
+                        "direction": "left",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "cigar",
+                            "dunhill"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "color",
+                            "blue"
+                        ],
+                        "B": [
+                            "name",
+                            "peter"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "bob"
+                        ],
+                        "B": [
+                            "flower",
+                            "tulips"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "place",
+                        "entity": [
+                            "name",
+                            "alice"
+                        ],
+                        "pos": 1
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "favoritesport",
+                            "baseball"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blue master"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "phonemodel",
+                            "google pixel 6"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "right",
+                        "dist": "?"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "carol"
+                        ],
+                        "B": [
+                            "favoritesport",
+                            "soccer"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "pos_relation",
+                        "A": [
+                            "flower",
+                            "carnations"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ],
+                        "direction": "left",
+                        "dist": "1"
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "name",
+                            "eric"
+                        ],
+                        "B": [
+                            "cigar",
+                            "blends"
+                        ]
+                    }
+                ]
+            ],
+            [
+                [
+                    {
+                        "type": "same_house",
+                        "A": [
+                            "favoritesport",
+                            "volleyball"
+                        ],
+                        "B": [
+                            "phonemodel",
+                            "iphone 13"
+                        ]
+                    }
+                ]
+            ]
+        ],
+        "solution_irs": [
+            [
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "alice"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "samsung galaxy s21"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "yellow monster"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "iris"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "red"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "baseball"
+                    ],
+                    "pos": 1
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "carol"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "oneplus 9"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blue master"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "carnations"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "green"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "soccer"
+                    ],
+                    "pos": 2
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "eric"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "xiaomi mi 11"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "blends"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "roses"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "yellow"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "tennis"
+                    ],
+                    "pos": 3
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "peter"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "iphone 13"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "dunhill"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "lilies"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "blue"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "volleyball"
+                    ],
+                    "pos": 4
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "arnold"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "huawei p50"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "prince"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "daffodils"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "purple"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "basketball"
+                    ],
+                    "pos": 5
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "name",
+                        "bob"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "phonemodel",
+                        "google pixel 6"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "cigar",
+                        "pall mall"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "flower",
+                        "tulips"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "color",
+                        "white"
+                    ],
+                    "pos": 6
+                },
+                {
+                    "type": "place",
+                    "entity": [
+                        "favoritesport",
+                        "swimming"
+                    ],
+                    "pos": 6
+                }
+            ]
+        ]
+    }
+}
\ No newline at end of file
diff --git a/interwhen/utils/zebralogic_helper.py b/interwhen/utils/zebralogic_helper.py
new file mode 100644
index 00000000..cde8a55b
--- /dev/null
+++ b/interwhen/utils/zebralogic_helper.py
@@ -0,0 +1,284 @@
+"""
+Prompt and dataset utilities for WildEval/ZebraLogic.
+"""
+
+import re
+import json
+from collections import defaultdict
+from typing import Dict, List, Tuple, Optional, Set
+from importlib import resources
+import datasets
+
+
+# ============== Prompt Templates ==============
+
+SYSTEM_PROMPT_VANILLA = """\
+# Problem Description
+
+You are solving a house grid problem. You are given:
+1. Features and Domains
+    - A fixed number of houses, indexed sequentially (e.g., House 1, House 2, …) from left to right.
+    - A set of features (e.g., color, name, pet, book genre).
+    - Each feature has a finite domain of possible values.
+2. Constraint:
+    - Each house has exactly one value per feature.
+    - No two houses share the same value for the same feature.
+3. Clues / Constraints descrbing:
+    - Houses and their positions
+    - Feature values
+    - Relative ordering (e.g., "next to", "to the left of", "2 houses away from")
+
+Solve to your best ability the arrangement of features across the houses.
+
+# Final Answer Format
+
+```json
+{
+    "House 1": { "feature1": "value1", "feature2": "value2", ... },
+    "House 2": { "feature1": "value1", "feature2": "value2", ... },
+    ...
+}
+```
+
+Make sure to use the exact feature/value names as given in the problem description.
+Make sure the JSON is valid and parsable."""
+
+SYSTEM_PROMPT_STATEPOLL = """\
+# Problem Description
+
+You are solving a house grid problem. You are given:
+1. Features and Domains
+    - A fixed number of houses, indexed sequentially (e.g., House 1, House 2, …) from left to right.
+    - A set of features (e.g., color, name, pet, book genre).
+    - Each feature has a finite domain of possible values.
+2. Constraint:
+    - Each house has exactly one value per feature.
+    - No two houses share the same value for the same feature.
+3. Clues / Constraints describing:
+    - Houses and their positions
+    - Feature values
+    - Relative ordering (e.g., "next to", "to the left of", "2 houses away from")
+
+# Rules for Solving
+
+1. Reason about the problem in text.
+2. After every inference, no matter how minor or tentative, immediately report the updated partial assignments.
+    - Always output partial assignments frequently as the reasoning progresses, not only at major steps or when confident.
+    - If an inference adds, removes, or narrows even a single possibility, report it.
+
+# House/Feature Partial Assignment Reporting Format
+
+```json
+{
+    "House N": { "feature1": "value1", "feature2": "value2", ... },
+    ...
+}
+```
+
+Omit any unassigned features.
+Make sure to use the exact feature/value names as given in the problem description.
+Make sure the JSON is valid and parsable."""
+
+SYSTEM_PROMPT_STATEFEEDBACK = """\
+# Problem Description
+
+You are solving a house grid problem. You are given:
+1. Features and Domains
+    - A fixed number of houses, indexed sequentially (e.g., House 1, House 2, …) from left to right.
+    - A set of features (e.g., color, name, pet, book genre).
+    - Each feature has a finite domain of possible values.
+2. Constraint:
+    - Each house has exactly one value per feature.
+    - No two houses share the same value for the same feature.
+3. Clues / Constraints describing:
+    - Houses and their positions
+    - Feature values
+    - Relative ordering (e.g., "next to", "to the left of", "2 houses away from")
+
+# Rules for Solving
+
+1. Reason about the problem in text.
+2. You may receive feedback from the user if anything is wrong. Use any feedback to guide your reasoning until a complete solution is reached.
+3. Do not stop responding until you've assigned each and every variable.
+
+# Final Answer Reporting Format
+
+```json
+{
+    "House 1": { "feature1": "value1", "feature2": "value2", ... },
+    "House 2": { "feature1": "value1", "feature2": "value2", ... },
+    ...
+}
+```
+
+Make sure to use the exact feature/value names as given in the problem description.
+Make sure the JSON is valid and parsable."""
+
+USER_PROMPT_TEMPLATE = "{problem_text}"
+
+# ============== Dataset Loading ==============
+
+def clean_problem_text(problem_text: str, features: dict) -> str:
+    """Clean up problem text giving explicit feature domains."""
+    desc, clues = problem_text.split('## clues:')
+    line0 = desc.splitlines()[0]
+
+    feature_text = ''
+    for feature, values in features.items():
+        values_str = ', '.join(f"'{v}'" for v in values)
+        feature_text += f"- '{feature}': {values_str}\n"
+
+    return f"{line0}\n{feature_text}\n## clues:{clues}".strip()
+
+
+def process_zebralogic_problem(problem: dict, ir_map: dict) -> dict:
+    """Process a raw ZebraLogic problem into the format needed by ZebraLogicProblem.
+
+    Args:
+        problem: Raw problem dict from the HuggingFace dataset.
+        ir_map: Dict mapping problem IDs to their IR representations.
+
+    Returns:
+        Processed problem dict with keys: n_houses, n_features, features, clues,
+        clue_irs, solution_irs, solution, puzzle_clean, etc.
+    """
+    def apply_text_replacements(problem):
+        replacements = [
+            ['january', 'jan'], ['february', 'feb'], ['march', 'mar'],
+            ['august', 'aug'], ['september', 'sept'], ['f-150', 'f150'],
+            ['animal', 'pet'], ['loves the spaghetti eater', 'loves spaghetti'],
+            ['very short', 'veryshort'], ['super short', 'supershort'],
+            ['very tall', 'verytall'], ['super tall', 'supertall'],
+        ]
+        problem_str = json.dumps(problem)
+        for old, new in replacements:
+            problem_str = problem_str.replace(old, new)
+        return json.loads(problem_str)
+
+    pid = problem['id']
+    size = problem["size"]
+    n_houses, n_features = map(int, size.split("*"))
+
+    problem_text = problem["puzzle"].lower()
+    clues_raw = re.split(r"##\s*clues\s*:", problem_text, flags=re.IGNORECASE)[1].strip().split("\n")
+    clues = []
+    for clue in clues_raw:
+        clue_text_index, clue_text = clue.strip().split(". ", 1)
+        clues.append({
+            "text_index": int(clue_text_index.strip()),
+            "text": clue_text.strip()
+        })
+
+    solution = problem["solution"]
+    solution['header'] = [h.lower() for h in solution['header']]
+    solution['rows'] = [[v.lower() for v in row] for row in solution['rows']]
+
+    features = defaultdict(list)
+    for row in solution['rows']:
+        for fname, value in zip(solution['header'], row):
+            if fname.lower() == 'house':
+                continue
+            features[fname].append(value)
+    features = dict(features)
+    for fname in features:
+        features[fname] = sorted(list(set(features[fname])))
+        assert len(features[fname]) == n_houses
+    assert len(features) == n_features
+
+    processed_solution = {f'House {i+1}': {} for i in range(n_houses)}
+    for house_i, row in enumerate(solution['rows']):
+        for fname, value in zip(solution['header'][1:], row[1:]):
+            processed_solution[f'House {house_i+1}'][fname.lower()] = value.lower()
+    problem['solution'] = processed_solution
+
+    problem['puzzle'] = problem_text
+    problem["clues"] = clues
+    problem["features"] = features
+    problem["n_houses"] = n_houses
+    problem["n_features"] = n_features
+    problem["clue_irs"] = ir_map[pid]["clue_irs"]
+    problem["solution_irs"] = ir_map[pid]["solution_irs"]
+    problem['puzzle_clean'] = clean_problem_text(problem['puzzle'], problem['features'])
+
+    return apply_text_replacements(problem)
+
+def get_zebralogic_dataset() -> list:
+    """Load and process the ZebraLogic dataset from HuggingFace.
+
+    Loads WildEval/ZebraLogic grid_mode test split and processes each problem
+    with the IR map.
+
+    The IR map file must be at interwhen/data/zebralogic_ir_map.json
+
+    Returns:
+        List of processed problem dicts.
+    """
+
+    dataset = datasets.load_dataset("WildEval/ZebraLogic", "grid_mode", split="test").to_list()
+
+    pkg = "interwhen.data"
+    with resources.files(pkg).joinpath("zebralogic_ir_map.json").open("r") as f:
+        ir_map = json.load(f)
+
+    # Known problematic problem IDs (unsolvable or malformed)
+    bad_ids = {
+        'lgp-test-6x5-2', 'lgp-test-6x6-5', 'lgp-test-2x5-1', 'lgp-test-4x5-5',
+        'lgp-test-2x4-6', 'lgp-test-2x6-11', 'lgp-test-4x6-35', 'lgp-test-3x5-15',
+        'lgp-test-5x5-37', 'lgp-test-5x5-17', 'lgp-test-4x5-15', 'lgp-test-6x6-2',
+        'lgp-test-5x6-4', 'lgp-test-5x6-2', 'lgp-test-5x5-1'
+    }
+    dataset = [p for p in dataset if p['id'] not in bad_ids]
+    dataset = [process_zebralogic_problem(p, ir_map) for p in dataset]
+    return dataset
+
+def extract_last_json(text):
+    """Extract the last JSON object from the model's output text."""
+    json_text = text.split('</think>')[-1].strip()
+    
+    # try with md tags
+    matches = re.findall(r'```json(.*?)```', json_text, re.DOTALL)
+    if matches and len(matches) > 0:
+        json_match = matches[-1]
+        return json.loads(json_match.strip())
+    
+    # try without assuming md tags
+    matches = re.findall(r'\{.*\}\s*?}', json_text, re.DOTALL)
+    if matches and len(matches) > 0:
+        json_match = matches[0]
+        return json.loads(json_match.strip())
+    
+    return None
+
+def zebra_correctness(problem: dict, candidate_solution: dict) -> Tuple[int, int, int, int]:
+    """Check candidate solution against ground truth.
+
+    Args:
+        problem: Processed problem dict with 'solution', 'n_houses', 'n_features', 'features'.
+        candidate_solution: Dict mapping "House N" -> {feature: value}.
+
+    Returns:
+        (correct, skipped, missing, total) counts where:
+            correct: Number of matching assignments
+            skipped: Assignments for invalid houses/features
+            missing: Features not in candidate solution
+            total: Total expected assignments (n_houses * n_features)
+    """
+    c, s = 0, 0
+    t_soln = 0
+    t = problem['n_houses'] * problem['n_features']
+    solution = problem['solution']
+
+    for house in candidate_solution:
+        if house not in solution:
+            s += len(problem['features'])
+            continue
+        for fname in candidate_solution[house]:
+            if fname not in solution[house]:
+                s += 1
+                continue
+            t_soln += 1
+            if candidate_solution[house][fname] == solution[house][fname]:
+                c += 1
+
+    m = t - t_soln
+    return c, s, m, t

From f424846ebe07f9fad757719d17e088e2dff55e45 Mon Sep 17 00:00:00 2001
From: ashmitkx <66110457+ashmitkx@users.noreply.github.com>
Date: Tue, 3 Mar 2026 12:38:35 +0000
Subject: [PATCH 05/11] add paralization accross dataset

---
 .../TTSwithVerification/bestofk_baseline.py   | 50 +++++++++++++------
 1 file changed, 34 insertions(+), 16 deletions(-)

diff --git a/examples/TTSwithVerification/bestofk_baseline.py b/examples/TTSwithVerification/bestofk_baseline.py
index a168ceec..ebfb6d39 100644
--- a/examples/TTSwithVerification/bestofk_baseline.py
+++ b/examples/TTSwithVerification/bestofk_baseline.py
@@ -1,10 +1,12 @@
 import argparse
 import asyncio
+from datetime import datetime
 import json
 import logging
 import os
 import re
 import sys
+from multiprocessing.pool import ThreadPool
 from contextlib import contextmanager
 from dataclasses import dataclass
 from typing import Dict, List, Optional
@@ -29,6 +31,9 @@
 
 logger = logging.getLogger(__name__)
 
+# Save the real stderr so tqdm always works even if suppress_output is active
+_real_stderr = sys.stderr
+
 
 @contextmanager
 def suppress_output():
@@ -720,6 +725,7 @@ def run_k_samples_with_critic(
     parser.add_argument("--seed", type=int, default=42, help="Base random seed")
     parser.add_argument("--max_tokens", type=int, default=32768, help="Max tokens for generation")
     parser.add_argument("--temperature", type=float, default=0.6, help="Sampling temperature")
+    parser.add_argument("--processes", "-p", type=int, default=1, help="Number of examples to process in parallel (default: 1, sequential)")
     parser.add_argument("--debug", "-d", action="store_true", help="Enable debug logging")
     args = parser.parse_args()
 
@@ -774,7 +780,8 @@ def run_k_samples_with_critic(
     total_tokens_all_samples = 0
     results = []
 
-    for idx in tqdm(indices, desc="Processing examples", unit="example"):
+    def process_example(idx):
+        """Process a single example: generate k samples, evaluate, return result dict."""
         example = dataset[int(idx)]
         if args.task == "game24":
             nums = example["numbers"]
@@ -837,17 +844,7 @@ def run_k_samples_with_critic(
 
         save_outputs(idx, sample_results, best_idx, output_dirs["reasoning"])
 
-        total_examples += 1
-        if any_correct:
-            total_correct += 1
-        total_correct_samples += correct_samples
-        total_samples += len(sample_results)
-        critic_correct_samples += critic_correct_samples_example
-        critic_total_samples += len(sample_results)
-        total_tokens += best_result.tokens
-        total_tokens_all_samples += sum(r.tokens for r in sample_results)
-
-        results.append({
+        return {
             "idx": int(idx),
             "best_idx": best_idx,
             "any_correct": any_correct,
@@ -862,10 +859,31 @@ def run_k_samples_with_critic(
             "all_critic_correct": [r.critic_correct for r in sample_results],
             "all_critic_feedback": [r.critic_feedback for r in sample_results],
             "options": options,
-        })
-
-        #logger.info(f"Best sample: {best_idx} | Correct in K: {any_correct}")
-        #logger.info(f"Best message: {best_result.message}")
+            "_any_correct": any_correct,
+            "_correct_samples": correct_samples,
+            "_critic_correct_samples": critic_correct_samples_example,
+            "_n_samples": len(sample_results),
+            "_best_tokens": best_result.tokens,
+            "_all_tokens_sum": sum(r.tokens for r in sample_results),
+        }
+
+    with ThreadPool(processes=args.processes) as pool:
+        for result in tqdm(pool.imap_unordered(process_example, indices), total=len(indices), desc="Processing examples", unit="example", file=_real_stderr):
+            total_examples += 1
+            if result["_any_correct"]:
+                total_correct += 1
+            total_correct_samples += result["_correct_samples"]
+            total_samples += result["_n_samples"]
+            critic_correct_samples += result["_critic_correct_samples"]
+            critic_total_samples += result["_n_samples"]
+            total_tokens += result["_best_tokens"]
+            total_tokens_all_samples += result["_all_tokens_sum"]
+
+            # Remove internal keys before appending
+            for k in list(result.keys()):
+                if k.startswith("_"):
+                    del result[k]
+            results.append(result)
 
     accuracy = total_correct / total_examples if total_examples else 0
     avg_best_tokens = total_tokens / total_examples if total_examples else 0

From ceaa92bbfe0fdca2874c7e33e9abceac8bd198d1 Mon Sep 17 00:00:00 2001
From: Vijval9 <114911861+Vijval9@users.noreply.github.com>
Date: Tue, 3 Mar 2026 23:20:34 +0530
Subject: [PATCH 06/11] Added verina (code) support to bestofk_baseline.py

Added Verina support and helper functions for evaluation.
---
 .../TTSwithVerification/bestofk_baseline.py   | 94 ++++++++++++++++++-
 1 file changed, 91 insertions(+), 3 deletions(-)

diff --git a/examples/TTSwithVerification/bestofk_baseline.py b/examples/TTSwithVerification/bestofk_baseline.py
index ebfb6d39..c17f4732 100644
--- a/examples/TTSwithVerification/bestofk_baseline.py
+++ b/examples/TTSwithVerification/bestofk_baseline.py
@@ -6,10 +6,13 @@
 import os
 import re
 import sys
+import shutil
+import subprocess
 from multiprocessing.pool import ThreadPool
 from contextlib import contextmanager
 from dataclasses import dataclass
-from typing import Dict, List, Optional
+from pathlib import Path
+from typing import Dict, List, Optional, Tuple
 
 import numpy as np
 import pandas as pd
@@ -21,13 +24,18 @@
 from interwhen.utils.zebralogic_helper import SYSTEM_PROMPT_VANILLA, USER_PROMPT_TEMPLATE, get_zebralogic_dataset, extract_last_json, zebra_correctness
 
 from interwhen import stream_completion
+from verina_utils import *
 
 # ============== MODEL CONFIGURATION ==============
 MAIN_MODEL = "Qwen/QwQ-32B"
 # Multi-process vLLM configuration
 VLLM_PORTS = [8000, 8001, 8002, 8003]  # 4 instances with tensor-parallel-size 2 each
 REQUEST_COUNTER = {"main": 0, "critic": 0}  # Track request count for round-robin load balancing
-
+# Verina paths
+_SCRIPT_DIR = Path(__file__).parent.resolve()
+VERINA_ROOT = (_SCRIPT_DIR / "../../../verina").resolve()
+VERINA_DATASETS_PATH = VERINA_ROOT / "datasets" / "verina"
+LEAN_PLAYGROUND_DIR = VERINA_ROOT / "lean-playground"
 
 logger = logging.getLogger(__name__)
 
@@ -332,6 +340,27 @@ def build_zebralogic_prompt(example):
     user_prompt = USER_PROMPT_TEMPLATE.format(problem_text=example['puzzle_clean'])
     return system_prompt, user_prompt
 
+# verina helpers
+def evaluate_verina_answer(output: str, data: BenchmarkData, task_idx: int) -> Tuple[bool, str, str]:
+    """Evaluate Verina code generation output - wrapper for best-of-k interface"""
+    generated_code = extract_code_from_response(output)
+    
+    if not generated_code.strip():
+        return False, "", "No code extracted from response"
+    
+    compiles, all_tests_pass, compile_output, test_results = evaluate_generated_code(data, generated_code, task_idx)
+    
+    num_tests = len(data.tests) if data.tests else 0
+    num_passed = sum(1 for v in test_results.values() if v == "pass")
+    
+    if compiles and all_tests_pass:
+        return True, generated_code, f"Code compiles and all {num_tests} tests pass"
+    elif compiles:
+        return False, generated_code, f"Compilation succeeded but {num_tests - num_passed}/{num_tests} tests failed"
+    else:
+        error_preview = compile_output[:300] if compile_output else "Unknown error"
+        return False, generated_code, f"Compilation failed: {error_preview}"
+
 
 def build_full_prompt(task, example, nums=None):
     if task == "game24":
@@ -341,6 +370,8 @@ def build_full_prompt(task, example, nums=None):
         system_prompt, user_prompt = build_maze_prompt(example)
     elif task == 'zebralogic':
         system_prompt, user_prompt = build_zebralogic_prompt(example)
+    elif task == "verina":
+        return build_verina_prompt(example)
     else:
         system_prompt, user_prompt = build_spatialmap_prompt(example)
     return (
@@ -359,6 +390,8 @@ def load_dataset_for_task(task):
         return load_dataset("microsoft/VISION_LANGUAGE", "spatial_map_text_only", split="val")
     if task == "zebralogic":
         return get_zebralogic_dataset()
+    if task == "verina":
+        return load_verina_dataset()
     raise ValueError(f"Unsupported task: {task}")
 
 
@@ -524,6 +557,52 @@ def build_mcq_critic_prompt(task, task_description, reasoning_output):
 If INCORRECT, explain what went wrong and suggest the correct approach.
 """
 
+def build_verina_critic_prompt(data: BenchmarkData, reasoning_output: str) -> str:
+    """Build critic prompt to evaluate Verina Lean code generation and provide reasoning."""
+    signature = data.signature
+    func_name = signature.get("name", "solution")
+    return_type = signature.get("return_type", "Bool")
+    param_list = render_param_list(signature)
+    
+    precond = data.lean_data.get("precond", "True").strip()
+    postcond = data.lean_data.get("postcond", "").strip()
+    
+    return f"""You are an expert Lean 4 code verifier. Evaluate the following code generation attempt.
+
+## Task Description
+{data.description}
+
+## Function Signature
+```lean4
+def {func_name} {param_list} (h_precond : {func_name}_precond ...) : {return_type}
+```
+
+## Precondition
+```lean4
+{precond}
+```
+
+## Postcondition
+```lean4
+{postcond}
+```
+
+## Student's Reasoning and Generated Code
+{reasoning_output}
+
+Verify:
+1. Is the generated code syntactically valid Lean 4?
+2. Does it match the expected function signature and return type ({return_type})?
+3. Does the logic appear to satisfy the postcondition given the precondition?
+4. Are there any obvious bugs, infinite loops, or incorrect base cases?
+
+Respond in the following format:
+VERDICT: CORRECT or INCORRECT
+REASONING: Your detailed explanation
+
+If CORRECT, briefly explain why
+If INCORRECT, explain what went wrong and suggest how to fix it.
+"""
 
 def batch_evaluate_with_critic(outputs_df, task, example, critic_llm_server, tokenizer, nums=None, quiet=True):
     """Batch evaluate outputs using vLLM API across multiple instances. Outputs_df should have columns: 'output', 'seed_idx'"""
@@ -573,6 +652,8 @@ async def _run_parallel():
                 elif task == "zebralogic":
                     _, task_desc = build_zebralogic_prompt(example)
                     critic_prompt = build_zebralogic_critic_prompt(task_desc, output_text)
+                elif task == "verina":
+                    critic_prompt = build_verina_critic_prompt(example, output_text)
                 else:
                     if task == "maze":
                         _, task_desc = build_maze_prompt(example)
@@ -704,7 +785,7 @@ def run_k_samples_with_critic(
 
 if __name__ == "__main__":
     parser = argparse.ArgumentParser(description="Best-of-K baseline (standard CoT) for TTSwithVerification datasets")
-    parser.add_argument("--task", type=str, required=True, choices=["game24", "maze", "spatialmap", "zebralogic"],
+    parser.add_argument("--task", type=str, required=True, choices=["game24", "maze", "spatialmap", "zebralogic","verina"],
                         help="Task to run")
     parser.add_argument("--k", type=int, default=4, help="Number of samples per example")
     parser.add_argument("--num_examples", "-n", type=int, default=None,
@@ -793,6 +874,13 @@ def process_example(idx):
             prompt = build_full_prompt(args.task, example)
             eval_fn = lambda output, ex=example: evaluate_zebralogic_answer(output, ex)
             options = None
+        elif args.task == "verina":
+            # For verina, example is a BenchmarkData object
+            prompt = build_full_prompt(args.task, example)
+            current_idx = int(idx)
+            current_data = example
+            eval_fn = lambda output, data=current_data, task_idx=current_idx: evaluate_verina_answer(output, data, task_idx)
+            options = None
         
         else:
             prompt = build_full_prompt(args.task, example)

From a0fbce4b7a4f6174b342313042b1a91ce73b380d Mon Sep 17 00:00:00 2001
From: Vijval9 <114911861+Vijval9@users.noreply.github.com>
Date: Tue, 3 Mar 2026 23:21:59 +0530
Subject: [PATCH 07/11] Added verina (code) utils

Add utility functions for Verina benchmark tasks, including loading data, parsing Lean files, and rendering unit tests.
---
 examples/TTSwithVerification/verina_utils.py | 649 +++++++++++++++++++
 1 file changed, 649 insertions(+)
 create mode 100644 examples/TTSwithVerification/verina_utils.py

diff --git a/examples/TTSwithVerification/verina_utils.py b/examples/TTSwithVerification/verina_utils.py
new file mode 100644
index 00000000..84db2338
--- /dev/null
+++ b/examples/TTSwithVerification/verina_utils.py
@@ -0,0 +1,649 @@
+import argparse
+import asyncio
+import json
+import logging
+import os
+import re
+import sys
+import shutil
+import subprocess
+from contextlib import contextmanager
+from dataclasses import dataclass
+from pathlib import Path
+from typing import Dict, List, Optional, Tuple
+import numpy as np
+import pandas as pd
+import aiohttp
+from datasets import load_dataset
+from tqdm import tqdm
+from transformers import AutoTokenizer
+
+__all__ = [
+    # Path constants
+    "VERINA_ROOT",
+    "VERINA_DATASETS_PATH", 
+    "LEAN_PLAYGROUND_DIR",
+    # Classes
+    "BenchmarkData",
+    # Constants
+    "CODE_TEST_MSG_MARKER",
+    "DECIDABLE_ERR_MSG",
+    # Functions
+    "parse_benchmark_lean_data",
+    "load_benchmark_data_from_task_dir",
+    "load_verina_dataset",
+    "render_param_list",
+    "build_verina_prompt",
+    "strip_function_definition",
+    "extract_code_from_response",
+    "create_lean_file",
+    "check_lean_compile",
+    "render_unit_test_value",
+    "render_code_unit_test",
+    "build_test_lean_file",
+    "parse_unit_test_results",
+    "evaluate_generated_code",
+]
+
+_SCRIPT_DIR = Path(__file__).parent.resolve()
+VERINA_ROOT = (_SCRIPT_DIR / "../../../verina").resolve()
+VERINA_DATASETS_PATH = VERINA_ROOT / "datasets" / "verina"
+LEAN_PLAYGROUND_DIR = VERINA_ROOT / "lean-playground"
+
+
+class BenchmarkData:
+    """Verina benchmark data structure"""
+    def __init__(self, data_id: str, description: str, signature: dict, 
+                 lean_data: dict, spec_desc: dict, tests: list, metadata: dict):
+        self.data_id = data_id
+        self.description = description
+        self.signature = signature  # {"name": str, "parameters": list, "return_type": str}
+        self.lean_data = lean_data  # contains task_imports, task_aux, code, precond, postcond, proof, etc.
+        self.spec_desc = spec_desc  # {"precond_desc": str, "postcond_desc": str}
+        self.tests = tests
+        self.metadata = metadata
+
+
+def parse_benchmark_lean_data(raw_lean_data: str) -> dict:
+    """Parse a .lean file with !benchmark markers into sections"""
+    lines = raw_lean_data.strip().splitlines()
+    
+    lean_data = {
+        "task_imports": "",
+        "solution_imports": "",
+        "task_aux": "",
+        "solution_aux": "",
+        "code_aux": "",
+        "precond_aux": "",
+        "postcond_aux": "",
+        "proof_aux": "",
+        "code": "",
+        "precond": "True",
+        "postcond": "",
+        "proof": "sorry",
+    }
+    
+    current_section = None
+    current_content = []
+    current_args = {}
+    
+    for line in lines:
+        if "-- !benchmark" in line:
+            marker_part = line.split("-- !benchmark", 1)[1].strip()
+            
+            if marker_part.startswith("@start"):
+                # Save previous section if any
+                if current_section is not None:
+                    content = "\n".join(current_content).strip()
+                    if current_section == "import":
+                        import_type = current_args.get("type", "task")
+                        if import_type == "task":
+                            lean_data["task_imports"] += content + "\n"
+                        elif import_type == "solution":
+                            lean_data["solution_imports"] += content + "\n"
+                    elif current_section in lean_data:
+                        lean_data[current_section] = content
+                
+                # Start new section
+                parts = marker_part.split("@start", 1)[1].strip().split(None, 1)
+                current_section = parts[0].strip()
+                current_args = {}
+                current_content = []
+                
+                if len(parts) > 1:
+                    for arg in parts[1].strip().split():
+                        if "=" in arg:
+                            key, value = arg.split("=", 1)
+                            current_args[key] = value
+                            
+            elif marker_part.startswith("@end"):
+                if current_section is not None:
+                    content = "\n".join(current_content).strip()
+                    if current_section == "import":
+                        import_type = current_args.get("type", "task")
+                        if import_type == "task":
+                            lean_data["task_imports"] += content + "\n"
+                        elif import_type == "solution":
+                            lean_data["solution_imports"] += content + "\n"
+                    elif current_section in lean_data:
+                        lean_data[current_section] = content
+                current_section = None
+                current_content = []
+                current_args = {}
+        else:
+            if current_section is not None:
+                current_content.append(line)
+    
+    return lean_data
+
+
+def load_benchmark_data_from_task_dir(task_dir: Path) -> Optional[BenchmarkData]:
+    """Load a single benchmark task from its directory"""
+    task_path = task_dir / "task.json"
+    if not task_path.exists():
+        return None
+    
+    try:
+        with open(task_path, "r") as f:
+            task_data = json.load(f)
+        
+        task_id = task_data.get("id")
+        if not task_id:
+            return None
+        
+        # Read description
+        desc_path = task_dir / task_data.get("description_file", "description.txt")
+        description = desc_path.read_text().strip() if desc_path.exists() else ""
+        
+        # Read signature
+        signature = task_data.get("signature", {})
+        
+        # Read lean file
+        lean_path = task_dir / task_data.get("lean_file", "task.lean")
+        if lean_path.exists():
+            lean_data = parse_benchmark_lean_data(lean_path.read_text())
+        else:
+            lean_data = {}
+        
+        # Read spec description
+        spec_desc = {
+            "precond_desc": task_data.get("specification", {}).get("preconditions", ""),
+            "postcond_desc": task_data.get("specification", {}).get("postconditions", ""),
+        }
+        
+        # Read tests
+        test_path = task_dir / task_data.get("test_file", "test.json")
+        tests = []
+        if test_path.exists():
+            with open(test_path, "r") as f:
+                tests = json.load(f)
+        
+        metadata = task_data.get("metadata", {})
+        
+        return BenchmarkData(
+            data_id=task_id,
+            description=description,
+            signature=signature,
+            lean_data=lean_data,
+            spec_desc=spec_desc,
+            tests=tests,
+            metadata=metadata,
+        )
+    except Exception as e:
+        return None
+
+
+def load_verina_dataset() -> List[BenchmarkData]:
+    """Load all verina benchmark tasks from the datasets directory"""
+    results = []
+    
+    # Get all task directories sorted by ID
+    task_dirs = sorted(
+        [d for d in VERINA_DATASETS_PATH.glob("verina_*") if d.is_dir()],
+        key=lambda x: (x.name.split("_")[1], int(x.name.split("_")[-1])),
+    )
+    
+    for task_dir in task_dirs:
+        data = load_benchmark_data_from_task_dir(task_dir)
+        if data:
+            results.append(data)
+    
+    return results
+
+
+def render_param_list(signature: dict) -> str:
+    """Render the parameter list for a function signature"""
+    params = signature.get("parameters", [])
+    rendered = ""
+    for param in params:
+        rendered += f"({param['param_name']} : {param['param_type']}) "
+    return rendered.strip()
+
+
+def build_verina_prompt(data: BenchmarkData) -> str:
+    """Build prompt for Verina Lean code generation (build_code_gen_prompt + build_full_prompt)"""
+    system_prompt = "You are an expert Lean 4 programmer. Generate valid Lean 4 code for the function body. Wrap your final code in [CODE] [/CODE] tags strictly."
+    
+    signature = data.signature
+    func_name = signature.get("name", "solution")
+    return_type = signature.get("return_type", "Bool")
+    param_list = render_param_list(signature)
+    params = signature.get("parameters", [])
+    
+    precond_name = f"{func_name}_precond"
+    param_names_str = ' '.join([f"({p['param_name']})" for p in params])
+    
+    # Get auxiliary definitions (only if they exist)
+    solution_aux = data.lean_data.get("solution_aux", "").strip()
+    task_aux = data.lean_data.get("task_aux", "").strip()
+    code_aux = data.lean_data.get("code_aux", "").strip()
+    precond = data.lean_data.get("precond", "True").strip()
+    postcond = data.lean_data.get("postcond", "").strip()
+    
+    # Build helper section only if there are helpers
+    helper_section = ""
+    all_aux = "\n".join(filter(None, [solution_aux, task_aux, code_aux]))
+    if all_aux:
+        helper_section = f"""
+## Helper Definitions
+```lean4
+{all_aux}
+```
+"""
+    
+    user_prompt = f"""## Task
+{data.description}
+
+## Function Signature
+```lean4
+def {func_name} {param_list} (h_precond : {precond_name} {param_names_str}) : {return_type} :=
+  -- YOUR CODE HERE (just output this part inside [CODE] [/CODE] tags)
+```
+
+## Precondition
+```lean4
+def {precond_name} {param_list} : Prop := {precond}
+```
+
+## Postcondition  
+```lean4
+def {func_name}_postcond {param_list} (result: {return_type}) : Prop := {postcond}
+```
+{helper_section}
+Provide ONLY the function body expression wrapped in [CODE]...[/CODE] tags."""
+
+    return (
+        f"<|im_start|>system\n{system_prompt}<|im_end|>\n"
+        f"<|im_start|>user\n{user_prompt}<|im_end|>\n"
+        f"<|im_start|>assistant\n"
+    )
+
+
+def strip_function_definition(code: str) -> str:
+    """
+    Strip function definition prefix if the model accidentally included it.
+    
+    The prompt asks for just the function body, but sometimes the model outputs:
+        def FunctionName (params) (h_precond : ...) : ReturnType :=
+          actual_body
+    
+    We need to extract just 'actual_body' and dedent it properly.
+    """
+    import textwrap
+    
+    code = code.strip()
+    
+    # Pattern to match Lean function definition:
+    # def <name> <params> (h_precond : <precond>) : <return_type> :=
+    # The function body follows after :=
+    func_def_pattern = r'^def\s+\w+\s+.*?:=[ \t]*\n?'
+    
+    match = re.match(func_def_pattern, code, re.DOTALL)
+    if match:
+        # Extract everything after the :=
+        body = code[match.end():]
+        # Dedent to remove common leading whitespace from all lines
+        body = textwrap.dedent(body).strip()
+        if body:
+            return body
+    
+    return code
+
+
+def extract_code_from_response(response: str) -> str:
+    """Extract code from the LAST [CODE]...[/CODE] tags or lean code blocks.
+    
+    Handles cases where:
+    1. Response has <think>...</think> reasoning block
+    2. [CODE] tag exists but [/CODE] may be missing (truncated response)
+    3. Code is in markdown lean blocks
+    4. Model outputs [CORE] or other variants instead of [CODE]
+    5. Model uses mismatched tags like [CORE]...[/CODE]
+    6. Model includes full function definition instead of just the body
+    """
+    # Step 1: Remove <think>...</think> block entirely (case insensitive)
+    # This prevents extracting reasoning text as code
+    cleaned = re.sub(r'<think>.*?</think>', '', response, flags=re.DOTALL | re.IGNORECASE)
+    
+    # If </think> exists but <think> doesn't match (partial), take everything after </think>
+    if not cleaned.strip() or cleaned.strip() == response.strip():
+        think_end = response.lower().rfind("</think>")
+        if think_end != -1:
+            cleaned = response[think_end + len("</think>"):]
+    
+    extracted_code = None
+    
+    # Step 2: Find the LAST closing tag [/CODE] or [/CORE] and work backwards to find opening tag
+    # This handles mismatched tags like [CORE]...[/CODE]
+    closing_pattern = r'\[/(?:CODE|CORE)\]'
+    closing_matches = list(re.finditer(closing_pattern, cleaned, re.IGNORECASE))
+    
+    if closing_matches:
+        # Get position of the last closing tag
+        last_close = closing_matches[-1]
+        close_pos = last_close.start()
+        
+        # Search backwards for the last opening tag before this closing tag
+        text_before_close = cleaned[:close_pos]
+        opening_pattern = r'\[(?:CODE|CORE|CORRECTED CODE)\]'
+        opening_matches = list(re.finditer(opening_pattern, text_before_close, re.IGNORECASE))
+        
+        if opening_matches:
+            last_open = opening_matches[-1]
+            extracted_code = cleaned[last_open.end():close_pos].strip()
+    
+    # Step 3: Try [CODE] without closing tag (truncated response) - find the LAST one
+    if extracted_code is None:
+        code_start_matches = list(re.finditer(r'\[(?:CODE|CORE|CORRECTED CODE)\]\s*', cleaned, re.DOTALL | re.IGNORECASE))
+        if code_start_matches:
+            # Get the last [CODE] tag position and extract everything after it
+            last_match = code_start_matches[-1]
+            code = cleaned[last_match.end():].strip()
+            # Remove any trailing incomplete text that looks like reasoning
+            # Stop at any line that looks like it's not code (e.g., starts with "Wait", "So", etc.)
+            lines = code.split('\n')
+            code_lines = []
+            for line in lines:
+                stripped = line.strip()
+                # Stop if we hit obvious non-code reasoning text
+                if stripped and re.match(r'^(Wait|So |But |Now|Note|The |This |However|Therefore|Thus|In |Since)', stripped):
+                    break
+                code_lines.append(line)
+            if code_lines:
+                extracted_code = '\n'.join(code_lines).strip()
+    
+    # Step 4: Try markdown lean code blocks (find the LAST one)
+    if extracted_code is None:
+        lean_matches = list(re.finditer(r'```lean4?\s*\n(.*?)```', cleaned, re.DOTALL | re.IGNORECASE))
+        if lean_matches:
+            extracted_code = lean_matches[-1].group(1).strip()
+    
+    # Step 5: Try lean block without closing (truncated) - find the LAST one
+    if extracted_code is None:
+        lean_start_matches = list(re.finditer(r'```lean4?\s*\n', cleaned, re.DOTALL | re.IGNORECASE))
+        if lean_start_matches:
+            last_match = lean_start_matches[-1]
+            code = cleaned[last_match.end():].strip()
+            # Remove trailing ``` if present
+            extracted_code = re.sub(r'```\s*$', '', code).strip()
+    
+    # Step 6: Last resort, return cleaned content if it looks like code
+    if extracted_code is None:
+        cleaned = cleaned.strip()
+        if cleaned:
+            # Filter out lines that look like reasoning
+            lines = cleaned.split('\n')
+            code_lines = []
+            for line in lines:
+                stripped = line.strip()
+                if stripped and not re.match(r'^(Wait|So |But |Now|Note|The |This |However|Therefore|Thus|In |Since|I |We |You )', stripped):
+                    code_lines.append(line)
+            if code_lines:
+                extracted_code = '\n'.join(code_lines).strip()
+    
+    # Step 7: Strip function definition prefix if model included it
+    # The prompt asks for just the body, but sometimes model outputs full "def ... :="
+    if extracted_code:
+        extracted_code = strip_function_definition(extracted_code)
+        return extracted_code
+    
+    return ""
+
+
+def create_lean_file(file_name: str, content: str) -> Path:
+    """Create a lean file in the playground directory"""
+    LEAN_PLAYGROUND_DIR.mkdir(parents=True, exist_ok=True)
+    lean_file = LEAN_PLAYGROUND_DIR / f"{file_name}.lean"
+    with open(lean_file, "w") as f:
+        f.write(content)
+    return lean_file
+
+
+def check_lean_compile(lean_file: Path, timeout: int = 120) -> Tuple[bool, str]:
+    """Check if the Lean file compiles successfully"""
+    try:
+        result = subprocess.run(
+            ["lake", "lean", str(lean_file)],
+            check=False,
+            stdout=subprocess.PIPE,
+            stderr=subprocess.PIPE,
+            timeout=timeout,
+            cwd=VERINA_ROOT,
+        )
+        
+        output = result.stdout.decode() + "\n" + result.stderr.decode()
+        
+        if result.returncode == 0:
+            return True, output
+        else:
+            return False, output
+            
+    except subprocess.TimeoutExpired:
+        return False, "TIMEOUT"
+    except Exception as e:
+        return False, f"ERROR: {e}"
+
+
+# Unit Test Rendering
+CODE_TEST_MSG_MARKER = "code_test"
+DECIDABLE_ERR_MSG = "did not evaluate to `true`"
+
+
+def render_unit_test_value(lean_type: str, value) -> str:
+    """Convert a Python value to Lean syntax based on type"""
+    if lean_type == "Bool":
+        return str(value).lower()
+    elif lean_type == "String":
+        return f'"{value}"'
+    elif lean_type == "Char":
+        return f"'{value}'"
+    else:
+        return str(value)
+
+
+def render_code_unit_test(signature: dict, test_case: dict, test_idx: int) -> str:
+    """Render a single unit test using #guard"""
+    func_name = signature.get("name", "solution")
+    params = signature.get("parameters", [])
+    return_type = signature.get("return_type", "Bool")
+    
+    rendered = f'#print "<{CODE_TEST_MSG_MARKER}>{test_idx}</{CODE_TEST_MSG_MARKER}>"\n\n'
+    rendered += f"#guard {func_name}"
+    
+    for param in params:
+        param_name = param["param_name"]
+        param_type = param["param_type"]
+        input_value = test_case["input"].get(param_name, "")
+        rendered += f" ({render_unit_test_value(param_type, input_value)})"
+    
+    # Add (by sorry) to satisfy precondition hypothesis
+    rendered += " (by sorry)"
+    
+    # Add expected value comparison
+    expected = test_case.get("expected", "")
+    rendered += f" == ({render_unit_test_value(return_type, expected)})"
+    
+    return rendered
+
+
+def build_test_lean_file(data: BenchmarkData, generated_code: str, include_unit_tests: bool = True) -> str:
+    """Build a complete Lean file to test the generated code"""
+    signature = data.signature
+    func_name = signature.get("name", "solution")
+    return_type = signature.get("return_type", "Bool")
+    param_list = render_param_list(signature)
+    params = signature.get("parameters", [])
+    param_names = " ".join([f"({p['param_name']})" for p in params])
+    
+    # Indent multiline generated_code so all lines have proper indentation
+    # First line gets 2 spaces from template, subsequent lines need explicit indentation
+    if '\n' in generated_code:
+        lines = generated_code.split('\n')
+        # First line has no extra indent (template adds 2 spaces)
+        # Subsequent lines need 2 spaces prepended
+        indented_lines = [lines[0]] + ['  ' + line if line.strip() else line for line in lines[1:]]
+        generated_code = '\n'.join(indented_lines)
+    
+    # Build imports - include both task and solution imports
+    task_imports = data.lean_data.get("task_imports", "").strip()
+    solution_imports = data.lean_data.get("solution_imports", "").strip()
+    imports = task_imports
+    if solution_imports:
+        imports += "\n" + solution_imports
+    if "import Mathlib" not in imports:
+        imports = "import Mathlib\n" + imports
+    
+    # Build auxiliary definitions - include solution_aux which has helper functions
+    solution_aux = data.lean_data.get("solution_aux", "").strip()
+    task_aux = data.lean_data.get("task_aux", "").strip()
+    precond_aux = data.lean_data.get("precond_aux", "").strip()
+    postcond_aux = data.lean_data.get("postcond_aux", "").strip()
+    code_aux = data.lean_data.get("code_aux", "").strip()
+    
+    # Build precondition
+    precond = data.lean_data.get("precond", "True").strip()
+    precond_name = f"{func_name}_precond"
+    
+    # Build postcondition
+    postcond = data.lean_data.get("postcond", "").strip()
+    postcond_name = f"{func_name}_postcond"
+    
+    lean_content = f"""{imports}
+
+-- Solution auxiliary definitions (helper functions)
+{solution_aux}
+
+-- Task auxiliary definitions
+{task_aux}
+
+-- Precondition auxiliary definitions
+{precond_aux}
+
+@[reducible, simp]
+def {precond_name} {param_list} : Prop :=
+  {precond}
+
+-- Postcondition auxiliary definitions
+{postcond_aux}
+
+-- Code auxiliary definitions
+{code_aux}
+
+def {func_name} {param_list} (h_precond : {precond_name} {param_names}) : {return_type} :=
+  {generated_code}
+
+@[reducible, simp]
+def {postcond_name} {param_list} (result: {return_type}) (h_precond : {precond_name} {param_names}) : Prop :=
+  {postcond}
+
+-- Verification theorem (compilation test)
+-- If this compiles, the code at least type-checks
+#check {func_name}
+"""
+    
+    # Add unit tests if requested
+    if include_unit_tests and data.tests:
+        lean_content += "\n-- Unit Tests\n"
+        for idx, test_case in enumerate(data.tests):
+            lean_content += "\n" + render_code_unit_test(signature, test_case, idx) + "\n"
+    
+    return lean_content
+
+
+def parse_unit_test_results(compile_output: str, num_tests: int) -> Tuple[int, int, dict]:
+    """
+    Parse the compilation output to determine which unit tests passed/failed.
+    
+    Returns: (num_passed, num_failed, test_results_dict)
+    """
+    test_results = {}
+    
+    # If compilation succeeded with no errors, all tests passed
+    if "error" not in compile_output.lower():
+        for idx in range(num_tests):
+            test_results[idx] = "pass"
+        return num_tests, 0, test_results
+    
+    # Parse the output to find which tests failed
+    # Look for markers like <code_test>0</code_test> followed by error messages
+    code_test_start = f"<{CODE_TEST_MSG_MARKER}>"
+    code_test_end = f"</{CODE_TEST_MSG_MARKER}>"
+    
+    # Split by start marker to get test sections
+    parts = compile_output.split(code_test_start)
+    
+    # Build a map of test index to message
+    test_messages = {}
+    for part in parts[1:]:  # Skip first part (before any marker)
+        if code_test_end in part:
+            idx_str, rest = part.split(code_test_end, 1)
+            try:
+                test_idx = int(idx_str.strip())
+                test_messages[test_idx] = rest
+            except ValueError:
+                continue
+    
+    num_passed = 0
+    num_failed = 0
+    
+    for idx in range(num_tests):
+        msg = test_messages.get(idx, "")
+        if DECIDABLE_ERR_MSG in msg:
+            test_results[idx] = "fail"
+            num_failed += 1
+        elif "error" in msg.lower():
+            # Some other error (e.g., type mismatch) - count as fail
+            test_results[idx] = "error"
+            num_failed += 1
+        else:
+            test_results[idx] = "pass"
+            num_passed += 1
+    
+    return num_passed, num_failed, test_results
+
+
+def evaluate_generated_code(data: BenchmarkData, generated_code: str, task_idx: int) -> Tuple[bool, bool, str, dict]:
+    """
+    Evaluate the generated code by compiling it with Lean and running unit tests.
+    
+    Returns: (compiles, all_tests_pass, output, test_results)
+    """
+    lean_content = build_test_lean_file(data, generated_code, include_unit_tests=True)
+    
+    # Create lean file
+    lean_file = create_lean_file(f"test_{data.data_id}_{task_idx}", lean_content)
+    
+    # Check compilation (which also runs unit tests via #guard)
+    compiles, output = check_lean_compile(lean_file)
+    
+    # Parse unit test results
+    num_tests = len(data.tests) if data.tests else 0
+    if num_tests > 0:
+        num_passed, num_failed, test_results = parse_unit_test_results(output, num_tests)
+        all_tests_pass = (num_failed == 0) and compiles
+    else:
+        # No tests, just check compilation
+        test_results = {}
+        all_tests_pass = compiles
+    
+    return compiles, all_tests_pass, output, test_results

From 7cab672de9aea2721e8f204ab49a460ec7c8a62c Mon Sep 17 00:00:00 2001
From: root
 <root@hp-reasoning-test-1node-7gpus-trainer-0.hp-reasoning-test-1node-7gpus.bonete11.svc.cluster.local>
Date: Wed, 4 Mar 2026 12:54:58 +0000
Subject: [PATCH 08/11] add fixes

---
 .../TTSwithVerification/bestofk_baseline.py   | 25 +++---
 examples/TTSwithVerification/check_tokens.py  | 27 ++++++
 .../start_vllm_multiprocess.sh                | 36 ++------
 .../test_maze_extraction.py                   | 86 +++++++++++++++++++
 examples/TTSwithVerification/test_vllm_api.py | 40 +++++++++
 5 files changed, 175 insertions(+), 39 deletions(-)
 create mode 100644 examples/TTSwithVerification/check_tokens.py
 create mode 100644 examples/TTSwithVerification/test_maze_extraction.py
 create mode 100644 examples/TTSwithVerification/test_vllm_api.py

diff --git a/examples/TTSwithVerification/bestofk_baseline.py b/examples/TTSwithVerification/bestofk_baseline.py
index 9b52206d..999ec6f8 100644
--- a/examples/TTSwithVerification/bestofk_baseline.py
+++ b/examples/TTSwithVerification/bestofk_baseline.py
@@ -19,9 +19,9 @@
 from interwhen import stream_completion
 
 # ============== MODEL CONFIGURATION ==============
-MAIN_MODEL = "Qwen/QwQ-32B"
+MAIN_MODEL = "Qwen/Qwen3-30B-A3B-Thinking-2507"
 # Multi-process vLLM configuration
-VLLM_PORTS = [8000, 8001, 8002, 8003]  # 4 instances with tensor-parallel-size 2 each
+VLLM_PORTS = [8000, 8001, 8002]  # 3 instances with tensor-parallel-size 2 each
 REQUEST_COUNTER = {"main": 0, "critic": 0}  # Track request count for round-robin load balancing
 
 
@@ -67,7 +67,7 @@ def get_next_port(server_type: str = "main") -> int:
     return port
 
 
-def get_output_dirs(task: str, main_model: str, use_critic: bool, critic_early_stop: bool, base_dir: str = "../../b-pchanda/Outputs_TTS/BestOfKResults"):
+def get_output_dirs(task: str, main_model: str, use_critic: bool, critic_early_stop: bool, base_dir: str = "../../b-pchanda/Outputs_TTS_temp/BestOfKResults"):
     model_short_name = get_model_short_name(main_model)
     critic_status = "on" if use_critic else "off"
     earlystop_status = "on" if critic_early_stop else "off"
@@ -82,26 +82,25 @@ def get_output_dirs(task: str, main_model: str, use_critic: bool, critic_early_s
             os.makedirs(dir_path, exist_ok=True)
     return dirs
 
-
-def init_llm_server(model_name, max_tokens=32768, port=8000, temperature=0.6, seed=42):
+def init_llm_server(modelname, max_tokens=200, port=8000, temperature=0.6, seed=42): #
     url = f"http://localhost:{port}/v1/completions"
     payload = {
-        "model": model_name,
+        "model": modelname,
         "max_tokens": max_tokens,
         "top_k": 20,
         "top_p": 0.95,
         "min_p": 0.0,
-        "do_sample": True,
+        "do_sample" : True,
         "temperature": temperature,
         "stream": False,
         "logprobs": 20,
         "use_beam_search": False,
         "prompt_cache": True,
-        "seed": seed,
+        "seed" : seed
     }
     headers = {"Content-Type": "application/json"}
     return {"url": url, "payload": payload, "headers": headers}
-
+ 
 
 def count_tokens(text: str, tokenizer) -> int:
     """Count tokens in text, with fallback to character count."""
@@ -346,7 +345,9 @@ def resolve_indices(task, dataset_len, args):
             except ValueError:
                 raise ValueError(f"Invalid xrange format: {args.xrange}. Use 'start-end'")
     if args.num_examples:
-        return np.linspace(0, dataset_len - 1, args.num_examples, dtype=int)
+        max_idx = dataset_len - 1
+        upper_bound = min(max_idx, 1362) if task == "game24" else min(max_idx, 1499)
+        return list((np.linspace(0, upper_bound, args.num_examples)).astype(int))
     # Default: use full range
     start = args.start if args.start is not None else 0
     end = args.end if args.end is not None else dataset_len
@@ -650,8 +651,8 @@ def run_k_samples_with_critic(
     parser = argparse.ArgumentParser(description="Best-of-K baseline (standard CoT) for TTSwithVerification datasets")
     parser.add_argument("--task", type=str, required=True, choices=["game24", "maze", "spatialmap"],
                         help="Task to run")
-    parser.add_argument("--k", type=int, default=4, help="Number of samples per example")
-    parser.add_argument("--num_examples", "-n", type=int, default=None,
+    parser.add_argument("--k", type=int, default=1, help="Number of samples per example")
+    parser.add_argument("--num_examples", "-n", type=int, default=100,
                         help="Number of examples to run (overrides start/end)")
     parser.add_argument("--indices", type=str, default=None,
                         help="Comma-separated indices to run")
diff --git a/examples/TTSwithVerification/check_tokens.py b/examples/TTSwithVerification/check_tokens.py
new file mode 100644
index 00000000..4380c194
--- /dev/null
+++ b/examples/TTSwithVerification/check_tokens.py
@@ -0,0 +1,27 @@
+#!/usr/bin/env python3
+"""Check what payload is actually being sent."""
+import requests
+import json
+
+url = "http://localhost:8000/v1/completions"
+payload = {
+    "model": "Qwen/QwQ-32B",
+    "prompt": "What is 2+2?",
+    "max_tokens": 50,
+    "temperature": 0.0,
+    "stream": False,
+}
+
+print("Payload being sent:")
+print(json.dumps(payload, indent=2))
+
+resp = requests.post(url, json=payload, timeout=10)
+result = resp.json()
+output = result["choices"][0]["text"]
+
+print(f"\nResponse usage:")
+print(f"  Tokens generated: {result['usage'].get('completion_tokens', '?')}")
+print(f"  Total tokens: {result['usage'].get('total_tokens', '?')}")
+
+print(f"\nOutput ({len(output)} chars):")
+print(repr(output))
diff --git a/examples/TTSwithVerification/start_vllm_multiprocess.sh b/examples/TTSwithVerification/start_vllm_multiprocess.sh
index 080b58b7..601918a2 100755
--- a/examples/TTSwithVerification/start_vllm_multiprocess.sh
+++ b/examples/TTSwithVerification/start_vllm_multiprocess.sh
@@ -1,12 +1,11 @@
 #!/bin/bash
 
-# Start 4 vLLM processes with explicit GPU assignment
-# Process 1: GPUs 0-1, Port 8000
-# Process 2: GPUs 2-3, Port 8001
-# Process 3: GPUs 4-5, Port 8002
-# Process 4: GPUs 6-7, Port 8003
+# Start 3 vLLM processes with explicit GPU assignment
+# Process 1: GPUs 0-1, Port 8000, TP=2
+# Process 2: GPUs 2-3, Port 8001, TP=2
+# Process 3: GPUs 4-5, Port 8002, TP=2
 
-MODEL="Qwen/QwQ-32B"
+MODEL="Qwen/Qwen3-30B-A3B-Thinking-2507"
 GPU_MEMORY=0.4
 TENSOR_PARALLEL=2
 
@@ -14,7 +13,7 @@ echo "Killing any existing vLLM processes..."
 pkill -9 -f "vllm.entrypoints.openai.api_server"
 sleep 2
 
-echo "Starting 4 vLLM processes..."
+echo "Starting 3 vLLM processes..."
 
 # Process 1 - GPUs 0,1
 (
@@ -62,31 +61,14 @@ sleep 5
 PID3=$!
 echo "Started Process 3 (GPUs 4-5, Port 8002) - PID: $PID3"
 
-sleep 5
-
-# Process 4 - GPUs 6,7
-(
-    export CUDA_VISIBLE_DEVICES=6,7
-    python -m vllm.entrypoints.openai.api_server \
-        --model $MODEL \
-        --port 8003 \
-        --tensor-parallel-size $TENSOR_PARALLEL \
-        --gpu-memory-utilization $GPU_MEMORY \
-        --disable-log-requests \
-        > /tmp/vllm_8003.log 2>&1
-) &
-PID4=$!
-echo "Started Process 4 (GPUs 6-7, Port 8003) - PID: $PID4"
-
 echo ""
-echo "All 4 vLLM processes started successfully."
-echo "Process PIDs: $PID1 $PID2 $PID3 $PID4"
+echo "All 3 vLLM processes started successfully."
+echo "Process PIDs: $PID1 $PID2 $PID3"
 echo ""
 echo "Log files:"
 echo "  /tmp/vllm_8000.log - Process 1"
 echo "  /tmp/vllm_8001.log - Process 2"
 echo "  /tmp/vllm_8002.log - Process 3"
-echo "  /tmp/vllm_8003.log - Process 4"
 echo ""
 echo "To stop all processes, run:"
 echo "  pkill -9 -f 'vllm.entrypoints.openai.api_server'"
@@ -95,4 +77,4 @@ echo "Waiting for processes to initialize (this may take 60-120 seconds)..."
 echo ""
 
 # Wait for all processes
-wait $PID1 $PID2 $PID3 $PID4
+wait $PID1 $PID2 $PID3
diff --git a/examples/TTSwithVerification/test_maze_extraction.py b/examples/TTSwithVerification/test_maze_extraction.py
new file mode 100644
index 00000000..bd5d4632
--- /dev/null
+++ b/examples/TTSwithVerification/test_maze_extraction.py
@@ -0,0 +1,86 @@
+#!/usr/bin/env python3
+"""Test maze/spatialmap extraction with real model output."""
+import requests
+import json
+import re
+from datasets import load_dataset
+
+def extract_solution_mcq(text):
+    """Current extraction function from baseline."""
+    patterns = [
+        r"\\boxed\{([^}]*)\}",  # \boxed{...}
+        r"boxed\{([^}]*)\}",     # boxed{...} without escape
+        r"\*\*([A-D])\*\*",      # **A** format
+        r"answer[:\s]*([A-D])",  # answer: A format
+        r"(?:^|\n)([A-D])(?:\s|$|\.)",  # Standalone letter
+    ]
+    
+    for pattern in patterns:
+        matches = re.findall(pattern, text, re.IGNORECASE)
+        if matches:
+            expr = matches[-1].strip()
+            choice_match = re.search(r"\b([ABCD])\b", expr, flags=re.IGNORECASE)
+            if choice_match:
+                return choice_match.group(1).upper()
+    
+    standalone = re.findall(r"\b([ABCD])\b", text)
+    if standalone:
+        return standalone[-1].upper()
+    
+    return None
+
+# Load maze dataset
+print("Loading maze dataset...")
+dataset = load_dataset("microsoft/VISION_LANGUAGE", "maze_text_only", split="val")
+example = dataset[0]
+
+# Build prompt like baseline does
+pre_prompt = (
+    "You are an expert problem solver. Carefully read the following multiple-choice question "
+    "and think through the solution step-by-step before providing your final answer. "
+    "Provide your final answer option by enclosing it within \\boxed{A/B/C/D}.:"
+)
+prompt_text = str(example.get("prompt", ""))[:500]  # First 500 chars
+
+full_prompt = f"<|im_start|>system\nYou are helpful.\n<|im_end|>\n<|im_start|>user\n{pre_prompt}\n\n{prompt_text}\n<|im_end|>\n<|im_start|>assistant\n"
+
+print(f"\nFull prompt:\n{full_prompt[:300]}...\n")
+
+# Test on port 8000
+url = "http://localhost:8000/v1/completions"
+payload = {
+    "model": "Qwen/QwQ-32B",
+    "prompt": full_prompt,
+    "max_tokens": 500,
+    "temperature": 0.6,
+    "stream": False,
+}
+
+print("Requesting model output...")
+resp = requests.post(url, json=payload, timeout=30)
+if resp.status_code == 200:
+    result = resp.json()
+    output = result["choices"][0].get("text", "")
+    print(f"\nModel output ({len(output)} chars):")
+    print("="*60)
+    print(output)
+    print("="*60)
+    
+    extracted = extract_solution_mcq(output)
+    print(f"\nExtraction result: {extracted}")
+    
+    # Try alternative patterns
+    print("\nTrying alternative extraction patterns:")
+    if "\\boxed{" in output:
+        print("  - Contains \\boxed{ pattern")
+    if r"\boxed{" in output or r"\\boxed{" in output:
+        print("  - Contains escaped boxed")
+    if re.search(r"[Aa]nswer[:\s]*([A-D])", output):
+        print("  - Found 'answer: X' pattern")
+    response_letters = re.findall(r"\b[A-D]\b", output)
+    if response_letters:
+        print(f"  - Found standalone letters: {response_letters}")
+
+else:
+    print(f"Error: {resp.status_code}")
+    print(resp.text[:500])
diff --git a/examples/TTSwithVerification/test_vllm_api.py b/examples/TTSwithVerification/test_vllm_api.py
new file mode 100644
index 00000000..eaf88430
--- /dev/null
+++ b/examples/TTSwithVerification/test_vllm_api.py
@@ -0,0 +1,40 @@
+#!/usr/bin/env python3
+"""Test vLLM API responses directly."""
+import requests
+import json
+
+# Test each port
+for port in [8000, 8001, 8002, 8003]:
+    print(f"\n{'='*60}")
+    print(f"Testing port {port}...")
+    print('='*60)
+    
+    url = f"http://localhost:{port}/v1/completions"
+    
+    # Test: simple completion
+    payload = {
+        "model": "Qwen/QwQ-32B",
+        "prompt": "What is 2+2? Answer:",
+        "max_tokens": 50,
+        "temperature": 0.0,
+        "stream": False,
+    }
+    
+    try:
+        resp = requests.post(url, json=payload, timeout=10)
+        print(f"Status: {resp.status_code}")
+        
+        if resp.status_code == 200:
+            result = resp.json()
+            print(f"Response keys: {result.keys()}")
+            if "choices" in result and len(result["choices"]) > 0:
+                choice = result["choices"][0]
+                text = choice.get("text", "")
+                print(f"Generated text: {repr(text[:100])}")
+                print(f"Text length: {len(text)}")
+            else:
+                print(f"No choices in response: {result}")
+        else:
+            print(f"Error response: {resp.text[:200]}")
+    except Exception as e:
+        print(f"Request failed: {e}")

From 9802544ad33bdf622424ea207f97bd9379022251 Mon Sep 17 00:00:00 2001
From: root
 <root@hp-reasoning-test-1node-7gpus-trainer-0.hp-reasoning-test-1node-7gpus.bonete11.svc.cluster.local>
Date: Wed, 4 Mar 2026 12:57:00 +0000
Subject: [PATCH 09/11] add new changes

---
 .gitignore | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.gitignore b/.gitignore
index d7b37631..43e0af15 100644
--- a/.gitignore
+++ b/.gitignore
@@ -200,6 +200,7 @@ cython_debug/
 #  refer to https://docs.cursor.com/context/ignore-files
 .*/Outputs_TTS/
 Outputs_TTS/
+Outputs_TTS_temp/
 .cursorignore
 .cursorindexingignore
 

From c8949172b2f8159cd6389b767cada7aa4cfcaa7a Mon Sep 17 00:00:00 2001
From: Vijval9 <114911861+Vijval9@users.noreply.github.com>
Date: Wed, 4 Mar 2026 18:46:16 +0530
Subject: [PATCH 10/11] Fixed some serialization issues

Added a custom JSON encoder to handle numpy types when dumping JSON.
---
 examples/TTSwithVerification/bestofk_baseline.py | 15 ++++++++++++++-
 1 file changed, 14 insertions(+), 1 deletion(-)

diff --git a/examples/TTSwithVerification/bestofk_baseline.py b/examples/TTSwithVerification/bestofk_baseline.py
index 5a545681..eb6aef3d 100644
--- a/examples/TTSwithVerification/bestofk_baseline.py
+++ b/examples/TTSwithVerification/bestofk_baseline.py
@@ -42,6 +42,19 @@
 # Save the real stderr so tqdm always works even if suppress_output is active
 _real_stderr = sys.stderr
 
+class NumpyEncoder(json.JSONEncoder):
+    """Custom JSON encoder that handles numpy types."""
+    def default(self, obj):
+        if isinstance(obj, np.bool_):
+            return bool(obj)
+        if isinstance(obj, np.integer):
+            return int(obj)
+        if isinstance(obj, np.floating):
+            return float(obj)
+        if isinstance(obj, np.ndarray):
+            return obj.tolist()
+        return super().default(obj)
+
 
 @contextmanager
 def suppress_output():
@@ -1006,5 +1019,5 @@ def process_example(idx):
 
     summary_path = os.path.join(output_dirs["base"], "summary.json")
     with open(summary_path, "w", encoding="utf-8") as f:
-        json.dump(summary, f, indent=2)
+        json.dump(summary, f, indent=2, cls=NumpyEncoder)
     # logger.info(f"Saved summary to {summary_path}")

From 4e72e1616940dd154b54f81127e1637c56010eef Mon Sep 17 00:00:00 2001
From: ashmitkx <66110457+ashmitkx@users.noreply.github.com>
Date: Tue, 17 Mar 2026 12:17:47 +0000
Subject: [PATCH 11/11] remove zebra setup code (added in different pr)

---
 interwhen/data/__init__.py            |      0
 interwhen/data/zebralogic_ir_map.json | 285374 -----------------------
 interwhen/utils/zebralogic_helper.py  |    284 -
 3 files changed, 285658 deletions(-)
 delete mode 100644 interwhen/data/__init__.py
 delete mode 100644 interwhen/data/zebralogic_ir_map.json
 delete mode 100644 interwhen/utils/zebralogic_helper.py

diff --git a/interwhen/data/__init__.py b/interwhen/data/__init__.py
deleted file mode 100644
index e69de29b..00000000
diff --git a/interwhen/data/zebralogic_ir_map.json b/interwhen/data/zebralogic_ir_map.json
deleted file mode 100644
index 2558c733..00000000
--- a/interwhen/data/zebralogic_ir_map.json
+++ /dev/null
@@ -1,285374 +0,0 @@
-{
-    "lgp-test-2x2-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "short"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "holly"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "short"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "april"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "holly"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "holly"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "pizza"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-38": {
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-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "oneplus 9"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "swimming"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "victorian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "milk"
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-                    "pos": 4
-                }
-            ]
-        ]
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-    "lgp-test-3x5-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cat"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "kailyn"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "craftsman"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "janelle"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "victorian"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
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-    "lgp-test-3x2-10": {
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-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "city"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "toyota camry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "iris"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "iris"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "meredith"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "samantha"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "alice"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "meredith"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "roses"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "milk"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "water"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blue"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "timothy"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "verytall"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "milk"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "city"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ranch"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "honda civic"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "short"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "city"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "associate"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "veryshort"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "photography"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "beach"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ford f150"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "high school"
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-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-28": {
-        "clue_irs": [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ]
-        ],
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
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-    "lgp-test-5x4-14": {
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-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bmw 3 series"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "stir fry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "prince"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
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-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
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-                            "huawei p50"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "lime"
-                        ],
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
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-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
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-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "tennis"
-                        ],
-                        "B": [
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-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
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-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blends"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "hamster"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "lime"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
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-                    }
-                ]
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
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-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
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-                        "pos": 4
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-                ]
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-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
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-                        "dist": "1"
-                    }
-                ]
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-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
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-                {
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-                },
-                {
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-                    "entity": [
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-                        "oneplus 9"
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-                },
-                {
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-                },
-                {
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-                    "entity": [
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-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "modern"
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "black"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
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-                    "pos": 4
-                },
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-                    "entity": [
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-                    "pos": 5
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "horse"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "huawei p50"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "brown"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "colonial"
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-                }
-            ]
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-    "lgp-test-6x4-29": {
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-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ]
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-                ]
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-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "place",
-                        "entity": [
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-                    }
-                ]
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                        "dist": 2
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-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                        "B": [
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-                            "coffee"
-                        ],
-                        "direction": "any",
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-                    }
-                ]
-            ]
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-                },
-                {
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-                },
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-                },
-                {
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-                    "entity": [
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-                },
-                {
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-                },
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-                },
-                {
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-                },
-                {
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-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 3
-                },
-                {
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-                },
-                {
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-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                        "mountain"
-                    ],
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-                },
-                {
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-                },
-                {
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-                    "entity": [
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "jan"
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-                },
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-                        "camping"
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-                },
-                {
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
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-                }
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
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-                            "classical"
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-                        "direction": "right",
-                        "dist": "?"
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-                ]
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-                        "A": [
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-                            "pop"
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-                        "B": [
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-                        "dist": "1"
-                    }
-                ]
-            ],
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-                        "type": "place",
-                        "entity": [
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-                            "bob"
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-                        "pos": 4
-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ]
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-                ]
-            ],
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-                        "A": [
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-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                            "jazz"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
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-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
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-                    "entity": [
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-                    "pos": 1
-                },
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-                    "entity": [
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-                },
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-                    "entity": [
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-                    "pos": 2
-                },
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                        "country"
-                    ],
-                    "pos": 4
-                },
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-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
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-                    "entity": [
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-                    "pos": 5
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "rock"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
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-    "lgp-test-6x4-31": {
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-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
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-                            "feb"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
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-                            "may"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "purple"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "supertall"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "supertall"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "samantha"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "supertall"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "master"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "holly"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "pizza"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
-                            "favoritesport",
-                            "volleyball"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "supertall"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "nurse"
-                    ],
-                    "pos": 1
-                },
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-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "horse"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "teacher"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tennis"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "soccer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "supertall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "doctor"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "basketball"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                }
-            ]
-        ]
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-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "meredith"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "april"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "purple"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "soup"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "pizza"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "samantha"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "alice"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "city"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "nationality",
-                            "chinese"
-                        ],
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-                        ],
-                        "B": [
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-                            "peter"
-                        ],
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-                        "dist": 2
-                    }
-                ]
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
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-                        ],
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-                ]
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 6
-                    }
-                ]
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-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
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-                    "entity": [
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-                        "tea"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
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-                    "type": "place",
-                    "entity": [
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-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "auburn"
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
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-                        "may"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "gray"
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-                },
-                {
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-                    "entity": [
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-                },
-                {
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-                {
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-                },
-                {
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
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-                    "type": "place",
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-                },
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-                    "type": "place",
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-                {
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-                    "type": "place",
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-                },
-                {
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
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-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
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-                        "dist": "?"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
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-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
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-                    {
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-                        "entity": [
-                            "nationality",
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-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "red"
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-                    }
-                ]
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ]
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-                        "entity": [
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-                            "blonde"
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-                    }
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-            [
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-                        "A": [
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-                        "A": [
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-                        ],
-                        "B": [
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-                            "dane"
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-                    }
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-                        ],
-                        "B": [
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-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
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-                            "gray"
-                        ]
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-                ]
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-                    "entity": [
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-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                    "entity": [
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-                {
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-                    "pos": 4
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-                {
-                    "type": "place",
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
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-                    "type": "place",
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-                },
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-                    "type": "place",
-                    "entity": [
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-                    "pos": 5
-                },
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-                    "type": "place",
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-                        "A": [
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-                            "carnations"
-                        ],
-                        "B": [
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-            ],
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-                        "type": "same_house",
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-                        ],
-                        "B": [
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-                            "iphone 13"
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-                        "A": [
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-                            "google pixel 6"
-                        ],
-                        "B": [
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-                            "roses"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                            "samsung galaxy s21"
-                        ],
-                        "B": [
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-                            "eric"
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-                        "A": [
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-                            "samsung galaxy s21"
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-                        "B": [
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-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
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-                ]
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-                        "type": "place",
-                        "entity": [
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-                            "alice"
-                        ],
-                        "pos": 1
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-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
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-                        ]
-                    }
-                ]
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-                },
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-                },
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-                },
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-                },
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-                },
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-                    "entity": [
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 3
-                },
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-                    "type": "place",
-                    "entity": [
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-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "craftsman"
-                        ],
-                        "B": [
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-                        ],
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-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                        ],
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-                        ],
-                        "direction": "left",
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-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                        ],
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-                    }
-                ]
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-                        ],
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-                    }
-                ]
-            ],
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-                        "A": [
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-                        ],
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-                        "A": [
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-                            "craftsman"
-                        ],
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-                        "dist": "?"
-                    }
-                ]
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-                        "type": "pos_relation",
-                        "A": [
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-                        ],
-                        "B": [
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-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
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-                },
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                        "craftsman"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
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-                    ],
-                    "pos": 3
-                },
-                {
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "milk"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "cigar",
-                            "yellow monster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "cigar",
-                            "yellow monster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ]
-        ],
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "cultural"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "baseball"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "camping"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cruise"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blends"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "volleyball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 6
-                }
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-    "lgp-test-3x6-15": {
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-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "high school"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
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-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "doctor"
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-                        "pos": 3
-                    }
-                ]
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-                        "type": "pos_relation",
-                        "A": [
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-                            "rock"
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-                        "B": [
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-                            "pop"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
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-                ]
-            ],
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-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
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-                        "pos": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ]
-        ],
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                    ],
-                    "pos": 2
-                },
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-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                    ],
-                    "pos": 2
-                },
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-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
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-                },
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                },
-                {
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-                    ],
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-                }
-            ]
-        ]
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-    "lgp-test-2x5-24": {
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-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
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-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
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-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
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-                {
-                    "type": "place",
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
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-                    ],
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-                },
-                {
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
-                    "type": "place",
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-                }
-            ]
-        ]
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-    "lgp-test-5x2-17": {
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-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
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-                            "ranch"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "penny"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                    "entity": [
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-                        "tennis"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "meredith"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "water"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "mediterranean"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "purple"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "master"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "purple"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "purple"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "trade school"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "soup"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "mediterranean"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "short"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "flower",
-                            "iris"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "german"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "blue"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "water"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "meredith"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "children",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "children",
-                            "alice"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "short"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "verytall"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "milk"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
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-                },
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-                    "entity": [
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-                        "oneplus 9"
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-                },
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-                    "type": "place",
-                    "entity": [
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-                        "milk"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
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-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
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-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "black"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "basketball"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "engineer"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 2
-                }
-            ]
-        ]
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-    "lgp-test-6x6-21": {
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-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "iris"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
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-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "black"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
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-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                            "water"
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-                        "B": [
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-                            "city"
-                        ]
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-                ]
-            ],
-            [
-                [
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-                        "type": "same_house",
-                        "A": [
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-                        "B": [
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-                            "carol"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
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-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
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-                            "carnations"
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-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "supertall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                            "lilies"
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-                        "B": [
-                            "name",
-                            "peter"
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-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
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-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "tulips"
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-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
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-                    "type": "place",
-                    "entity": [
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-                        "alice"
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-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                {
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-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 1
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-                {
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-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
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-                    "entity": [
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-                        "roses"
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-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                    "pos": 3
-                },
-                {
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-                        "cultural"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
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-                },
-                {
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-                    "entity": [
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
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-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "auburn"
-                    ],
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-                },
-                {
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-                },
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-                    "entity": [
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-                },
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-                    "entity": [
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-                },
-                {
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
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-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                        "camping"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
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-                }
-            ]
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
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-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "bob"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                            "high school"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "arnold"
-                        ],
-                        "B": [
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-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "colonial"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "bachelor"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                        "type": "same_house",
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-                },
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-                },
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-                    ],
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-                },
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-                },
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-                },
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-                },
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-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "hip hop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "sarah"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "trade school"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "flower",
-                            "iris"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
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-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "flower",
-                            "iris"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "mediterranean"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "flower",
-                            "iris"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "supertall"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "supertall"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "samantha"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "short"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "holly"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "trade school"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                            "coffee"
-                        ],
-                        "B": [
-                            "education",
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-                        ],
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-                    }
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-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "coffee"
-                        ],
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-                    }
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-                    "type": "place",
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-                },
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-                },
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "science fiction"
-                    ],
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-                },
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-                    "entity": [
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-                },
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-                    "entity": [
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-                        "trade school"
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-                },
-                {
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-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "auburn"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "historical fiction"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
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-                        "master"
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-                },
-                {
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-                    "entity": [
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-                        "water"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blonde"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
-                    "type": "place",
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-                        "veryshort"
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-                    "pos": 5
-                },
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-                    "type": "place",
-                    "entity": [
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-                        "bachelor"
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-                },
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-                    "type": "place",
-                    "entity": [
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-                },
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-                    "type": "place",
-                    "entity": [
-                        "name",
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-                },
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-                    "type": "place",
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-                        "black"
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-                },
-                {
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-                    "entity": [
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-                        "fantasy"
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-                },
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-                },
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-                    "entity": [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "photography"
-                        ],
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
-                        "name",
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
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-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-37": {
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-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "yellow"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "classical"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
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-                ]
-            ],
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-                        "A": [
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-                            "holly"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
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-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 3
-                },
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-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cherry"
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-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                        "aniya"
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-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                        "pop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                }
-            ]
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-    "lgp-test-5x6-35": {
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-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "roses"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "milk"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "mother",
-                            "sarah"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "sarah"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "iris"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "iris"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "meredith"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "mediterranean"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "sarah"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "april"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "education",
-                            "trade school"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "trade school"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "trade school"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "sarah"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ]
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "mystery"
-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
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-                },
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-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                        "daffodils"
-                    ],
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-                },
-                {
-                    "type": "place",
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "associate"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
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-    "lgp-test-5x4-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bachelor"
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-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tulips"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tennis"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "master"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "daffodils"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
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-    "lgp-test-6x3-22": {
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-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "artist"
-                        ],
-                        "B": [
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-                            "doctor"
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-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                        "type": "not_place",
-                        "entity": [
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-                        ],
-                        "pos": 6
-                    }
-                ]
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-                        "type": "place",
-                        "entity": [
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-                        "pos": 5
-                    }
-                ]
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
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-                        "A": [
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-                            "horse"
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-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
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-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "rabbit"
-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "artist"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                }
-            ]
-        ]
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-    "lgp-test-3x4-0": {
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-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "swede"
-                        ],
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "brit"
-                        ],
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "cat"
-                        ],
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "science fiction"
-                        ],
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-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "mystery"
-                        ],
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
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-                            "romance"
-                        ]
-                    }
-                ]
-            ]
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-                },
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-                },
-                {
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-                },
-                {
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-                },
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-                    ],
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-                },
-                {
-                    "type": "place",
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                }
-            ]
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-    },
-    "lgp-test-5x2-0": {
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "hamster"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "roses"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
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-                        "grilled cheese"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "nationality",
-                            "chinese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "short"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "nationality",
-                            "chinese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "german"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "city"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "samantha"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "pizza"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "roses"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "flower",
-                            "iris"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "iris"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
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-                        "type": "pos_relation",
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-                    "entity": [
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-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "honda civic"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "short"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "spaghetti"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
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-    "lgp-test-4x5-24": {
-        "clue_irs": [
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-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
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-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "mystery"
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-                }
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-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "doctorate"
-                        ],
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
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-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "doctorate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "woodworking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                        "swimming"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                        "bachelor"
-                    ],
-                    "pos": 4
-                },
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-                    "entity": [
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-                        "baseball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "painting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "master"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "volleyball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "trade school"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "basketball"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
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-    "lgp-test-3x4-30": {
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
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-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "meredith"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "water"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "water"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "nurse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "coffee"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "lawyer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "root beer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "boba tea"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "engineer"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-17": {
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-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "iris"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "doctor"
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-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "lime"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "baseball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
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-    "lgp-test-6x5-30": {
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-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
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-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "boba tea"
-                        ],
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-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "not_place",
-                        "entity": [
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-                            "soup"
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-                ]
-            ],
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                            "spaghetti"
-                        ],
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "beach"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "soup"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "left",
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-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                            "tall"
-                        ],
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-                    }
-                ]
-            ],
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-                        "A": [
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-                        "B": [
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-                            "coffee"
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-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "carol"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
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-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "soup"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
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-                        "cultural"
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
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-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tea"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "mountain"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "stir fry"
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-                },
-                {
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-                },
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-                },
-                {
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-                    "entity": [
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-                    "pos": 5
-                },
-                {
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-                    "entity": [
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-                        "city"
-                    ],
-                    "pos": 5
-                },
-                {
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-                    "entity": [
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-                    ],
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-                },
-                {
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                },
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-                    "entity": [
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-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 6
-                },
-                {
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-                    "pos": 6
-                },
-                {
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-                    "entity": [
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-                        "root beer"
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
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-                }
-            ]
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-    "lgp-test-2x4-30": {
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
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-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "brown"
-                    ],
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-                },
-                {
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-                    "entity": [
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-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "desert"
-                    ],
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-                },
-                {
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-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cherry"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
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-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "city"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
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-                        "A": [
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-                            "bob"
-                        ],
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-                        "type": "not_place",
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-                },
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-                        "type": "same_house",
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-                        "A": [
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-                    }
-                ]
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-                },
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-                },
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-                },
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "education",
-                            "trade school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "trade school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "pizza"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "victorian"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "mediterranean"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "pizza"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "short"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "trade school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "mother",
-                            "sarah"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "flower",
-                            "iris"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "sarah"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "april"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "supertall"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "pizza"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
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-                        "type": "same_house",
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-                        "A": [
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-                        ],
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-                            "education",
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-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 1
-                },
-                {
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-                },
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-                },
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-                },
-                {
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-                },
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-                },
-                {
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-                    "entity": [
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-                },
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-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
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-                },
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-                },
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-                },
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-                    "entity": [
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-                },
-                {
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "name",
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-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
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-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
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-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ]
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-                {
-                    "type": "place",
-                    "entity": [
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-                },
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-                },
-                {
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-                    "entity": [
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-                },
-                {
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-                },
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-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "victorian"
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-                }
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    ],
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-                },
-                {
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-                        "type": "pos_relation",
-                        "A": [
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-                            "modern"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
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-                    }
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-                        "type": "same_house",
-                        "A": [
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-                            "colonial"
-                        ]
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-                        "A": [
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-                        ],
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-                        "dist": "?"
-                    }
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-                        "A": [
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-                ]
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-                        "A": [
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-                    }
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-                        "type": "pos_relation",
-                        "A": [
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-                            "name",
-                            "bob"
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-                        "dist": 2
-                    }
-                ]
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-                {
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
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-                    ],
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-                },
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
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-                    ],
-                    "pos": 2
-                },
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-                    "entity": [
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-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                },
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-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
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-                    "pos": 5
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-                    "pos": 6
-                },
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-                        "type": "not_place",
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-                    }
-                ]
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-                        ],
-                        "B": [
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-                        ],
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-                    }
-                ]
-            ],
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-                        "B": [
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-                    }
-                ]
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-                        ],
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-                        ]
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-                ]
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-                        "entity": [
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-                    }
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-                        "B": [
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-                        "A": [
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-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ]
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-                    ],
-                    "pos": 1
-                },
-                {
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-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    ],
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-                },
-                {
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-                        "pizza"
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-                    "pos": 1
-                },
-                {
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                },
-                {
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "pall mall"
-                    ],
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-                },
-                {
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-                    ],
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-                },
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-                },
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-                },
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-                },
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-                },
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-                },
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-                }
-            ]
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-                        "type": "same_house",
-                        "A": [
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-                            "master"
-                        ],
-                        "B": [
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-                        ]
-                    }
-                ]
-            ],
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-                        "entity": [
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-                        ],
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
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-                        ],
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                        ],
-                        "B": [
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-                            "master"
-                        ],
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-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
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-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                        ],
-                        "B": [
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-                        ],
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-                        "dist": "1"
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "swede"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "city"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "mediterranean"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "iris"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "short"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "pizza"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "soup"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "soup"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "trade school"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "trade school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "city"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "april"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "city"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "water"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
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-                        "dist": 2
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "fred"
-                        ],
-                        "B": [
-                            "children",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "timothy"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "timothy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bmw 3 series"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "toyota camry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ford f150"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "iris"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "meredith"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "timothy"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
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-                            "modern"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "craftsman"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "swimming"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "modern"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "basketball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "mediterranean"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "purple"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "iris"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "milk"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "supertall"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "penny"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "penny"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "sarah"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "city"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "city"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 6
-                }
-            ]
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-    "lgp-test-6x3-5": {
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-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 2
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-                ]
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-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "pos": 2
-                    }
-                ]
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                            "swede"
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-                ]
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "white"
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-                        "B": [
-                            "nationality",
-                            "norwegian"
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-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "german"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "yellow"
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-                    "pos": 6
-                }
-            ]
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
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-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
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-                        ],
-                        "B": [
-                            "favoritesport",
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "soccer"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
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-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "cherry"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "colonial"
-                    ],
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-                {
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-                        "tennis"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cherry"
-                    ],
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-                },
-                {
-                    "type": "place",
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-                        "average"
-                    ],
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-                },
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "veryshort"
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-                    "pos": 3
-                }
-            ]
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-    "lgp-test-5x6-25": {
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
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-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
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-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "dunhill"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "desert"
-                        ],
-                        "B": [
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-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
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-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "oneplus 9"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "holly"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "supertall"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "sarah"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "penny"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "soup"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "trade school"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "trade school"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "trade school"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "average"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "nationality",
-                            "chinese"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "samantha"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "meredith"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "april"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "short"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "supertall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "supertall"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "milk"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "short"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "master"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "blue"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "purple"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "water"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "blue"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "purple"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "pizza"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "blue"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "mediterranean"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "sarah"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "meredith"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "april"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "mediterranean"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "sarah"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "master"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
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-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
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-                ]
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-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "bachelor"
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-                    }
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
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-            ],
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-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "trade school"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
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-                        "dist": "?"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "trade school"
-                        ],
-                        "B": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
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-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
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-                },
-                {
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-                    "entity": [
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-                        "german"
-                    ],
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-                },
-                {
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-                    "entity": [
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-                {
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-                    "entity": [
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-                    "pos": 2
-                },
-                {
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                },
-                {
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-                    "entity": [
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-                        "associate"
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-                    "pos": 2
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-                },
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-                        "rock"
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-                },
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-                },
-                {
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-                        "brit"
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-                },
-                {
-                    "type": "place",
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-                        "country"
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-                    "entity": [
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-                        "peter"
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-                    "pos": 5
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-                {
-                    "type": "place",
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-                    "pos": 5
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-                    "entity": [
-                        "musicgenre",
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-                },
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-                },
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-                    "entity": [
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-                    "pos": 6
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-                {
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-                {
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-                },
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
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-                ]
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-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
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-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
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-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
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-                        "A": [
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-                            "toyota camry"
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-                        "B": [
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-                            "swimming"
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-                        "entity": [
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-                        "A": [
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-                        "B": [
-                            "musicgenre",
-                            "rock"
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-                    }
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-                        "type": "same_house",
-                        "A": [
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-                        "B": [
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-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
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-                        "direction": "left",
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-                        "A": [
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-                        "A": [
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-                            "rock"
-                        ],
-                        "direction": "right",
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-                    }
-                ]
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-                    "entity": [
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-                },
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-                },
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-                {
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-                    "pos": 2
-                },
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-                    "pos": 2
-                },
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-                },
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-                    "entity": [
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-                },
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-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
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-                        "B": [
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-                            "daffodils"
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-                        "A": [
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-                        "dist": "?"
-                    }
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-                        ],
-                        "B": [
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-                        ],
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-                        "dist": "1"
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-                ]
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-                        "entity": [
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-                    }
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-                },
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-                ]
-            ],
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-                    }
-                ]
-            ],
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-                    }
-                ]
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-                            "black"
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-                    }
-                ]
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-                },
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-                },
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-                },
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-                },
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-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "master"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "holly"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "mediterranean"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "water"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "blue"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
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-                    "entity": [
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-                    "entity": [
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-                        "bob"
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-                },
-                {
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-                    "entity": [
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-                },
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-                },
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-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "huawei p50"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "stir fry"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "doctorate"
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-                },
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-                    "type": "place",
-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "samsung galaxy s21"
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-                },
-                {
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-                    "entity": [
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-                        "pizza"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
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-                },
-                {
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-                        "cruise"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "master"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "associate"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 5
-                }
-            ]
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-    "lgp-test-5x3-21": {
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-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                    }
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
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-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
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-                            "bmw 3 series"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "prince"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                        "bmw 3 series"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "honda civic"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blends"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "toyota camry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "children",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "watermelon"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                        "type": "place",
-                        "entity": [
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-                            "lime"
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-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "mar"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
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-                        "dist": "?"
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-                ]
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-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
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-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
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-                ]
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-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
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-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
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-                            "gray"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
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-                        "entity": [
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-            ],
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-                        "type": "same_house",
-                        "A": [
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-                            "sarah"
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-                        "B": [
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-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
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-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "jan"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blueberry"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                    ],
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-                },
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-                    "entity": [
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-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                        "kailyn"
-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "fred"
-                    ],
-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
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-                        "A": [
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-                        "A": [
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-                        "type": "pos_relation",
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-                            "name",
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-                    }
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-                },
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-                },
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-                {
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-                    "type": "place",
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
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-                },
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-                    "type": "place",
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-                },
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-                    "type": "place",
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-                    {
-                        "type": "place",
-                        "entity": [
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-                    }
-                ]
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-                        "type": "pos_relation",
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-                            "hobby",
-                            "woodworking"
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-                    }
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-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
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-                        "B": [
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-                        ]
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
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-                            "victorian"
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-                        "dist": 3
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-                        "B": [
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-                    }
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-                        "A": [
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-                        "type": "same_house",
-                        "A": [
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-                        "type": "place",
-                        "entity": [
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-                            "country"
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-                        "B": [
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-                            "colonial"
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-                        "dist": 2
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-                ]
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-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
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-                ]
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-                        "type": "same_house",
-                        "A": [
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-            ],
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-                        "type": "place",
-                        "entity": [
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-                ]
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-                    "type": "place",
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-                },
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-                        "B": [
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-                    }
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-                        "A": [
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-                    }
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-            ],
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-                        "entity": [
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-                ]
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-                        "dist": "?"
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-                ]
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-                        "type": "same_house",
-                        "A": [
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-                        "B": [
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-                        ]
-                    }
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-                    {
-                        "type": "place",
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-                        "type": "not_place",
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-                ]
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-                        "entity": [
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-                        "A": [
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-                ]
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-                        "type": "same_house",
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-                },
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-                },
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-                },
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-                },
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-                },
-                {
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-                },
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-                },
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-                },
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-                },
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-                },
-                {
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "roses"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "pizza"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 1
-                },
-                {
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-                        "A": [
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-                ]
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-                        "A": [
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-                        ]
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-                ]
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-                ]
-            ],
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-                        "A": [
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-                ]
-            ],
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-                        ]
-                    }
-                ]
-            ],
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-                ]
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-                        ],
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-                ]
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-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "verytall"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "sarah"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "doctor"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "sept"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "victorian"
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-                },
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-                    "type": "place",
-                    "entity": [
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-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "pall mall"
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-                }
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-    "lgp-test-5x5-33": {
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-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "dunhill"
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-                    }
-                ]
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-                        "type": "pos_relation",
-                        "A": [
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-                            "rock"
-                        ],
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-                            "musicgenre",
-                            "classical"
-                        ],
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-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ]
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-                ]
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
-                            "musicgenre",
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-            [
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-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "dunhill"
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-                        "A": [
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-                            "jazz"
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-                        "B": [
-                            "cigar",
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-                        "A": [
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-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
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-                        "dist": 1
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-                ]
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-                        "type": "pos_relation",
-                        "A": [
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-                            "pall mall"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
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-                        "dist": 3
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
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-                ]
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-                        "type": "pos_relation",
-                        "A": [
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-                            "coffee"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
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-                        "dist": "?"
-                    }
-                ]
-            ],
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-                        "A": [
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-                            "norwegian"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                            "water"
-                        ],
-                        "B": [
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-                            "blends"
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-                        "dist": 2
-                    }
-                ]
-            ],
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-                        "A": [
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-                            "alice"
-                        ],
-                        "B": [
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-                            "tea"
-                        ]
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-                    "entity": [
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-                    ],
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-                },
-                {
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-                    ],
-                    "pos": 1
-                },
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-                        "pop"
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-                {
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-                },
-                {
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-                        "pall mall"
-                    ],
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-                },
-                {
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-                },
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "brit"
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-                    "pos": 2
-                },
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
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-                },
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-                },
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-                        "dunhill"
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-                },
-                {
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-                    "entity": [
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-                {
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-                {
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-                {
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-                },
-                {
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-                },
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-                        "A": [
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-                        "entity": [
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-                        "A": [
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-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
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-                        ]
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-                },
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-                },
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-                },
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-                },
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-                        "A": [
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-                            "samsung galaxy s21"
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-                        "A": [
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-                },
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-                },
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-                },
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-                },
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "oneplus 9"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "supertall"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "short"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "april"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "pizza"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "country"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "B": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "sarah"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "samantha"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
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-                    }
-                ]
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-                        "A": [
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-                            "roses"
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-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
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-                        "entity": [
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-                        "A": [
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-                    }
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-                            "city"
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-                    }
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-            ],
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-                        "type": "same_house",
-                        "A": [
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-                            "arnold"
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-                        "B": [
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-                            "oneplus 9"
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-                        "A": [
-                            "vacation",
-                            "city"
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-                        "B": [
-                            "flower",
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ]
-        ],
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-                    "type": "place",
-                    "entity": [
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-                        "eric"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
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-                },
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-                        "city"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "google pixel 6"
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-                },
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-                    "type": "place",
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-                        "cruise"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "daffodils"
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-                        "alice"
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-                },
-                {
-                    "type": "place",
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-                        "iphone 13"
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-                },
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-                },
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-                        "arnold"
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-                },
-                {
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-                    "entity": [
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-                        "oneplus 9"
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-                },
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "lilies"
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-    "lgp-test-6x3-4": {
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-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
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-                ]
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                ]
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "bob"
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-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
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-                ]
-            ],
-            [
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-                        "A": [
-                            "haircolor",
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-                        "B": [
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-                            "doctor"
-                        ]
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-            ],
-            [
-                [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        "B": [
-                            "haircolor",
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-                        "A": [
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-                            "doctor"
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-                            "name",
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-                    }
-                ]
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-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
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-                        "B": [
-                            "name",
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-                        "dist": "1"
-                    }
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-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
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-                        "B": [
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-                    }
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-                            "bob"
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-                        "B": [
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-                            "teacher"
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-                        "dist": "1"
-                    }
-                ]
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
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-                        "B": [
-                            "haircolor",
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-                        ],
-                        "direction": "right",
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-            [
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-                        "type": "not_place",
-                        "entity": [
-                            "name",
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-            ],
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-                        "A": [
-                            "haircolor",
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-                        "B": [
-                            "name",
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-                        ]
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-                ]
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-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
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-                        "direction": "left",
-                        "dist": "?"
-                    }
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-                    "entity": [
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-                },
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-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                },
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-                    "entity": [
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-                    "pos": 2
-                },
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-                    "entity": [
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-                },
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-                },
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-                },
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-                },
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-                    "entity": [
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-                },
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-                },
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-                },
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-                },
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-                    "pos": 5
-                },
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-                    "entity": [
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-                    "pos": 6
-                },
-                {
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-                    "entity": [
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-                    "pos": 6
-                },
-                {
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-                }
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-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
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-                ]
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-                        "type": "same_house",
-                        "A": [
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-                            "stir fry"
-                        ],
-                        "B": [
-                            "housestyle",
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-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "alice"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
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-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        "B": [
-                            "food",
-                            "stew"
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-                        "A": [
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-                ]
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-                        "entity": [
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-                        "A": [
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-                        "B": [
-                            "food",
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-                        "A": [
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-                        "dist": 2
-                    }
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-                        "type": "same_house",
-                        "A": [
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-                            "mountain"
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-                        "B": [
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-                            "yellow monster"
-                        ]
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-                        "A": [
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-                        "B": [
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-                        "B": [
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-                        "A": [
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-                    }
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-                    }
-                ]
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-                        "B": [
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-                    }
-                ]
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-                        "type": "pos_relation",
-                        "A": [
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-                            "grilled cheese"
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-                ]
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-                            "cruise"
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-                        "direction": "left",
-                        "dist": "?"
-                    }
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-                },
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-                },
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                },
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-                    "pos": 2
-                },
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-                },
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-                    ],
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-                },
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "mediterranean"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "milk"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "april"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "cigar",
-                            "yellow monster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "volleyball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "volleyball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "sarah"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "city"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
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-                        "dist": "1"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "painting"
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-                    }
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                        "toyota camry"
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-                },
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-                },
-                {
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-                },
-                {
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-                    "entity": [
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-                },
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
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-                    ],
-                    "pos": 4
-                },
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-                    "type": "place",
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-                        "knitting"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "woodworking"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bmw 3 series"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
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-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "gardening"
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-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
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-            [
-                [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
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-                        "A": [
-                            "name",
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-                        "B": [
-                            "musicgenre",
-                            "pop"
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-                        "dist": "1"
-                    }
-                ]
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-                        "A": [
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-                        "B": [
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-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
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-                        "B": [
-                            "musicgenre",
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-                        ]
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-                        "A": [
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-                            "fish"
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-                        "B": [
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-                            "arnold"
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-                        "dist": "?"
-                    }
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-                },
-                {
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-                    "entity": [
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-                },
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-                }
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-    "lgp-test-6x2-34": {
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-                        "type": "not_place",
-                        "entity": [
-                            "name",
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-                    }
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-                        "entity": [
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-                            "height",
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-                        "entity": [
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-                        "B": [
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-                        "entity": [
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-                    }
-                ]
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-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
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-                            "swede"
-                        ],
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-                        ],
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-                        "dist": "1"
-                    }
-                ]
-            ],
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-                        "entity": [
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-                    }
-                ]
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-            [
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-                        "type": "same_house",
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-                        "B": [
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-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "not_place",
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-                        ],
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-                    }
-                ]
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-                        "dist": 3
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-                ]
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-                },
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-                },
-                {
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-                },
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-                },
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-                },
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-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "april"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "timothy"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "master"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "trade school"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "trade school"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "education",
-                            "trade school"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "trade school"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "soup"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "mediterranean"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "desert"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
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-    "lgp-test-2x3-17": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
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-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "lime"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "norwegian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "brit"
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-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                        "mystery"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "xiaomi mi 11"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dane"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "desert"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "biography"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cherry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "iphone 13"
-                    ],
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-                }
-            ]
-        ]
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-    "lgp-test-5x3-2": {
-        "clue_irs": [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
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-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "root beer"
-                        ],
-                        "B": [
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-                            "eric"
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-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
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-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "water"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "bob"
-                        ],
-                        "B": [
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-                            "painting"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "gardening"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "root beer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "painting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "photography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "soup"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "iris"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "pizza"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "painting"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
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-    "lgp-test-6x4-14": {
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-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "mother",
-                            "sarah"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "sarah"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
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-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "honda civic"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "woodworking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "chevrolet silverado"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "aniya"
-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bmw 3 series"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "painting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "toyota camry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cooking"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
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-    "lgp-test-4x5-21": {
-        "clue_irs": [
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "toyota camry"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
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-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
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-                        "B": [
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-                            "roses"
-                        ]
-                    }
-                ]
-            ],
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-                        "entity": [
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-                            "watermelon"
-                        ],
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-                    }
-                ]
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-                        "A": [
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-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "swimming"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "honda civic"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "mystery"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "holly"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blue"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "honda civic"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "green"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "penny"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-24": {
-        "clue_irs": [
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-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "jan"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "april"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-38": {
-        "clue_irs": [
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-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
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-                        "type": "not_place",
-                        "entity": [
-                            "name",
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-                    }
-                ]
-            ],
-            [
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-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
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-                            "modern"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    ],
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-                },
-                {
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-                },
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "swede"
-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
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-                    ],
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-                },
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-                    "entity": [
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-                        "peter"
-                    ],
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-                },
-                {
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-                    "entity": [
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-                        "gray"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "german"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "april"
-                    ],
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-                },
-                {
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
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-                },
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-                },
-                {
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-                },
-                {
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-                },
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-                },
-                {
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-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
-                    "type": "place",
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "modern"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "samantha"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "city"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
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-                },
-                {
-                    "type": "place",
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-                },
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-                    "type": "place",
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-                },
-                {
-                    "type": "place",
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-                        "huawei p50"
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-                },
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-                    "type": "place",
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-                },
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-                        "bob"
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-                },
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-                        "A": [
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-                        "A": [
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-                            "blonde"
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-                        "A": [
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-                            "eric"
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-                        "B": [
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-                        "dist": "?"
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-                        "B": [
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-                    }
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-                        "dist": "1"
-                    }
-                ]
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-                        "type": "not_place",
-                        "entity": [
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-                            "cat"
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-                    }
-                ]
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-                    ],
-                    "pos": 1
-                },
-                {
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-                },
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                },
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
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-                    ],
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-                },
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-                },
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-                },
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-                },
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-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ford f150"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "penny"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "purple"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "country"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "iris"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "april"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "milk"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "woodworking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-12": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-11": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "iris"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "trade school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "holly"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-13": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "iris"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "purple"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "purple"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "sarah"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "white"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-33": {
-        "clue_irs": [
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-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
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-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
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-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-8": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
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-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
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-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "root beer"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "coffee"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "fish"
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-                    "pos": 5
-                }
-            ]
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-    "lgp-test-6x2-24": {
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "name",
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-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "cultural"
-                        ],
-                        "B": [
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-                            "city"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
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-                        "pos": 4
-                    }
-                ]
-            ],
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-                        "type": "not_place",
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-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
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-                        "A": [
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-                        ],
-                        "B": [
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-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                        ],
-                        "B": [
-                            "name",
-                            "carol"
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-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                            "mountain"
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-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
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-                        "B": [
-                            "name",
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-                        ],
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-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
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-                        ],
-                        "B": [
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-                            "camping"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
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-                    "type": "place",
-                    "entity": [
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-                        "peter"
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-                },
-                {
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-                },
-                {
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-                    "entity": [
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-                },
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-                },
-                {
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-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
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-                    ],
-                    "pos": 4
-                },
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-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
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-                },
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-                    "entity": [
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-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                }
-            ]
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-    "lgp-test-6x5-16": {
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
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-                    }
-                ]
-            ],
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-                        "type": "not_place",
-                        "entity": [
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-                            "dog"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "brit"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                        ],
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-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
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-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
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-                        ],
-                        "pos": 2
-                    }
-                ]
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-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "nationality",
-                            "chinese"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "biography"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
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-                            "science fiction"
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-                    }
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-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
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-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "norwegian"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ]
-                    }
-                ]
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-                [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "dane"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
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-                            "romance"
-                        ]
-                    }
-                ]
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-                    "entity": [
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-                },
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-                    ],
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-                },
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-                    "entity": [
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-                {
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-                },
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
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-                },
-                {
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-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "rabbit"
-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "biography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "historical fiction"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "water"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "penny"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "blue"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "knitting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "trade school"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "education",
-                            "trade school"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
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-                {
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-                },
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-                    "type": "place",
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-                },
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-                },
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-                    "entity": [
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-                        "rabbit"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "mediterranean"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "carol"
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-                },
-                {
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-                    "entity": [
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-                },
-                {
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "grilled cheese"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bachelor"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "horse"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "victorian"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "trade school"
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cat"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "craftsman"
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-                    "pos": 6
-                }
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-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ]
-                    }
-                ]
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-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
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-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
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-                        "type": "not_place",
-                        "entity": [
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-                            "tea"
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-                    }
-                ]
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-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
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-                            "occupation",
-                            "doctor"
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-                        "A": [
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-                            "iphone 13"
-                        ],
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-                            "drink",
-                            "coffee"
-                        ]
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-                        "A": [
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-                            "engineer"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ]
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-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
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-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "stew"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
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-                        "engineer"
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-                },
-                {
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-                },
-                {
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-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                        "stir fry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "spaghetti"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
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-                        "tea"
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "pizza"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ford f150"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "lawyer"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "milk"
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-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                        "peter"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tesla model 3"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "huawei p50"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "teacher"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                }
-            ]
-        ]
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-    "lgp-test-6x5-5": {
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "doctorate"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "master"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
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-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
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-                        "type": "pos_relation",
-                        "A": [
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-                            "supertall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
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-                        "dist": "?"
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-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "watermelon"
-                        ],
-                        "pos": 6
-                    }
-                ]
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-                        "A": [
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-                        ],
-                        "B": [
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-                            "desert"
-                        ]
-                    }
-                ]
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-            [
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-                        "A": [
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-                        ],
-                        "B": [
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-                        "A": [
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-                        ],
-                        "B": [
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-                        "type": "same_house",
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-                            "lime"
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-                            "hamster"
-                        ]
-                    }
-                ]
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-                        "type": "place",
-                        "entity": [
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-                        ],
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-                    }
-                ]
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-                        "type": "same_house",
-                        "A": [
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-                            "blueberry"
-                        ],
-                        "B": [
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-                            "trade school"
-                        ]
-                    }
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-                        "type": "pos_relation",
-                        "A": [
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-                            "veryshort"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
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-                        "dist": "?"
-                    }
-                ]
-            ]
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
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-                },
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-                    "entity": [
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-                    ],
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-                },
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-                    "entity": [
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
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-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                },
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-                    "entity": [
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-                },
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-                    "entity": [
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-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
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-                    ],
-                    "pos": 3
-                },
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-                    "type": "place",
-                    "entity": [
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-                        "doctorate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "soup"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "soup"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "knitting"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "knitting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "timothy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "stir fry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "woodworking"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bella"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "stew"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "pop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "april"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-0": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x3-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-21": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "supertall"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-36": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "water"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cat"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "daffodils"
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-                    "pos": 2
-                }
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "april"
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-                    }
-                ]
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-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
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-            [
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-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
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-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 1
-                },
-                {
-                    "type": "place",
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-                        "april"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "city"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
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-                    "pos": 3
-                }
-            ]
-        ]
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-    "lgp-test-6x3-1": {
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
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-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
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-                        "pos": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
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-                            "teacher"
-                        ]
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-                ]
-            ],
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-                        "A": [
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-                            "artist"
-                        ],
-                        "B": [
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-                            "fantasy"
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-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "romance"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                        "teacher"
-                    ],
-                    "pos": 2
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-                {
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-                    "entity": [
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-                        "romance"
-                    ],
-                    "pos": 2
-                },
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-                    "type": "place",
-                    "entity": [
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-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
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-                    ],
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-                },
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-                    "entity": [
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-                    "pos": 4
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-                    "type": "place",
-                    "entity": [
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-                        "artist"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "mystery"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
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-                        "historical fiction"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
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-                {
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-            ]
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-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
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-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "name",
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-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "spaghetti"
-                        ],
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-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
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-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
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-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "water"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
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-                    "type": "place",
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-                },
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-                },
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-                },
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-                    "entity": [
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-                        "alice"
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-                },
-                {
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-                    "entity": [
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-                        "tea"
-                    ],
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-                },
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-                },
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-                    "entity": [
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-                    "entity": [
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-                },
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-                },
-                {
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-                }
-            ]
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-                        "type": "same_house",
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-                            "basketball"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "not_place",
-                        "entity": [
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-                            "engineer"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
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-                        "A": [
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-                            "eric"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                        ],
-                        "B": [
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-                            "pop"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "soccer"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                        "pop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
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-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
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-    "lgp-test-2x5-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "german"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "german"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "desert"
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-                }
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "verytall"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                        ],
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
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-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "modern"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "craftsman"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "craftsman"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
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-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "craftsman"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "baseball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "camping"
-                    ],
-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                        "ranch"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "basketball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "verytall"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "city"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                }
-            ]
-        ]
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-    "lgp-test-3x6-3": {
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "science fiction"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x5-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "soup"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "stew"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "may"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-6": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-20": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "blueberry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "soup"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 3
-                },
-                {
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 6
-                }
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-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
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-                        "direction": "left",
-                        "dist": "?"
-                    }
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
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-                        "dist": 3
-                    }
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-                        "type": "same_house",
-                        "A": [
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-                        "B": [
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-                        "A": [
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-                        "type": "same_house",
-                        "A": [
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-                            "swede"
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-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
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-                        "type": "pos_relation",
-                        "A": [
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-                        "B": [
-                            "name",
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-                        ],
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-                        "dist": "?"
-                    }
-                ]
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-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "nationality",
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-                        ]
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
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-                ]
-            ],
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-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
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-                    }
-                ]
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "classical"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "jazz"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "pop"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "norwegian"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "hip hop"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "brit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 5
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-                    "type": "place",
-                    "entity": [
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                }
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
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-                            "lime"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "A": [
-                            "food",
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-                            "eric"
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-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
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-            [
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-                        "A": [
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-                            "dane"
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-                        "direction": "left",
-                        "dist": "1"
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-                ]
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-                        "A": [
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-                        "A": [
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-                        "B": [
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-                        "A": [
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-                            "name",
-                            "peter"
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-                        "direction": "any",
-                        "dist": 2
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-                    "type": "place",
-                    "entity": [
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-                    "entity": [
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-                    "entity": [
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-                },
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-                    "entity": [
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-                },
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-                    ],
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-                        "lime"
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-                },
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-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
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-                        "swede"
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-                    "pos": 4
-                },
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-                    "type": "place",
-                    "entity": [
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-                        "pizza"
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-                    "pos": 4
-                },
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-                    "type": "place",
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-                },
-                {
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-                    "entity": [
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-                    "pos": 5
-                },
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-                },
-                {
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-                        "type": "not_place",
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-                ]
-            ],
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-                    {
-                        "type": "place",
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-                        ],
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-                    }
-                ]
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-                            "pall mall"
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-                        "direction": "any",
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-                    }
-                ]
-            ],
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-                        "type": "place",
-                        "entity": [
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-                    }
-                ]
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-                        "B": [
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-                        ],
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
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-                            "mother",
-                            "janelle"
-                        ]
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-                ]
-            ],
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-                        "type": "not_place",
-                        "entity": [
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-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
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-                        "B": [
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-                        ]
-                    }
-                ]
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-                    "type": "place",
-                    "entity": [
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-                },
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-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                },
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-                    "entity": [
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-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
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-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x5-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "meredith"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-35": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "trade school"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-18": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "timothy"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "ranch"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x6-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "trade school"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "historical fiction"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "high school"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "fantasy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "fred"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "basketball"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
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-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "samantha"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                        "volleyball"
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "trade school"
-                    ],
-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                        "baseball"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bachelor"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "historical fiction"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bella"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tennis"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
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-    "lgp-test-2x2-30": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
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-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "birthday",
-                            "may"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "not_place",
-                        "entity": [
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-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
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-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
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-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
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-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "jan"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "huawei p50"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "jan"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "mar"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "blueberry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "carol"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "blueberry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "mother",
-                            "holly"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "fantasy"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x5-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "horse"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "watermelon"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "bird"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x2-23": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-15": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x6-29": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "april"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x2-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "children",
-                            "samantha"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "meredith"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "associate"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "high school"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-16": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-24": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "rock"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "soup"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "food",
-                            "pizza"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "stew"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-7": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "education",
-                            "trade school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "volleyball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "education",
-                            "trade school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "doctorate"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "associate"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "trade school"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-2x4-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x3-19": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "master"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "education",
-                            "master"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "romance"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-9": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
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-                        "dist": 1
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-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "B": [
-                            "name",
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-                        "A": [
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-                        ],
-                        "B": [
-                            "name",
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-                        ],
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
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-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
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-            ],
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-                        "type": "place",
-                        "entity": [
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-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
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-                        ],
-                        "B": [
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-                            "fish"
-                        ],
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-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
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-                    }
-                ]
-            ],
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-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
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-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
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-                ]
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-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
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-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                    ],
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-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "black"
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "rabbit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
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-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "fish"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
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-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
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-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
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-                    "pos": 6
-                }
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-    "lgp-test-3x5-28": {
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-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        "B": [
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-                            "soccer"
-                        ]
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-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
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-                            "desert"
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-                        "dist": "1"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "basketball"
-                        ],
-                        "B": [
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-                            "city"
-                        ],
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-                        "dist": "1"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                    }
-                ]
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-                        "type": "pos_relation",
-                        "A": [
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-                        ],
-                        "B": [
-                            "name",
-                            "peter"
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-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
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-                    }
-                ]
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-                        "type": "same_house",
-                        "A": [
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-                            "cherry"
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-                        "B": [
-                            "nationality",
-                            "dane"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
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-            ]
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-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
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-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
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-                    "entity": [
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-                        "city"
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-                    "pos": 2
-                },
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-                },
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-                    "pos": 3
-                },
-                {
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-                {
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
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-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "any",
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-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
-                            "pet",
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-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
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-                            "ranch"
-                        ]
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-                ]
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-                        "type": "place",
-                        "entity": [
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-                ]
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-            [
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
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-                        "A": [
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-                        "B": [
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-                        "entity": [
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-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                            "holly"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "janelle"
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "kailyn"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
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-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ]
-                    }
-                ]
-            ]
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-                    "type": "place",
-                    "entity": [
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-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                {
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-                    "entity": [
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-                    "pos": 2
-                },
-                {
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-                    "pos": 2
-                },
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-                    "entity": [
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-                },
-                {
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-                },
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-                },
-                {
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-                    "entity": [
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-                        "aniya"
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-                        "A": [
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-                        ],
-                        "B": [
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-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        ],
-                        "B": [
-                            "nationality",
-                            "brit"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
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-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "dane"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
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-                    "pos": 1
-                },
-                {
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-                },
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-                    "entity": [
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-                {
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-                }
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-                    }
-                ]
-            ],
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-                        "A": [
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-                        ],
-                        "B": [
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-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                        ],
-                        "B": [
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-                            "doctor"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
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-                {
-                    "type": "place",
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-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                },
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-                    "entity": [
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-                },
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-                }
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-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
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-                            "dog"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                            "tennis"
-                        ],
-                        "B": [
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-                            "average"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "cat"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "baseball"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "not_place",
-                        "entity": [
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-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
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-                        "dist": 2
-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                            "cat"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                        "A": [
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-                            "rabbit"
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-                        "B": [
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-                        "dist": "?"
-                    }
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-            ],
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-                        "A": [
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-                        "B": [
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-                            "dunhill"
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-                ]
-            ],
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-                        "A": [
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-                            "red"
-                        ],
-                        "B": [
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-                            "dunhill"
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-            ],
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-                        "type": "not_place",
-                        "entity": [
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-                        "A": [
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-                        ],
-                        "B": [
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-                    }
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-            ],
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-                        "A": [
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-                        "type": "pos_relation",
-                        "A": [
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-                        "B": [
-                            "haircolor",
-                            "black"
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-                        "dist": "1"
-                    }
-                ]
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-                        "A": [
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-                        "type": "same_house",
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-                        "B": [
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-                ]
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-                        "type": "pos_relation",
-                        "A": [
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-                            "bob"
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-                            "fish"
-                        ],
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-                        "dist": 1
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-                ]
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-                        "type": "same_house",
-                        "A": [
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-                            "dunhill"
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-                        "B": [
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-                ]
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
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-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                        "B": [
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-                            "prince"
-                        ]
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-                ]
-            ],
-            [
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-                        "A": [
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-                            "blonde"
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-                        "B": [
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-                            "tall"
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-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                            "swimming"
-                        ],
-                        "B": [
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-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "supertall"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
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-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                            "horse"
-                        ],
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-                    }
-                ]
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-                        "type": "pos_relation",
-                        "A": [
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-                            "cat"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ]
-        ],
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-                        "peter"
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-                },
-                {
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-                },
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-                        "pall mall"
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-                },
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-                },
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-                },
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-                },
-                {
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-                },
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-                            "name",
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-                        ],
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-                            "rock"
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-                ]
-            ],
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-                        "entity": [
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-                ]
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-                ]
-            ],
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-                        "entity": [
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-                ]
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-                ]
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-                    ],
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-                },
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-                },
-                {
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-                },
-                {
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-                },
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-                },
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-                },
-                {
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-                }
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
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-                        ]
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-                ]
-            ],
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-                        ],
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-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
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-                        ],
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-                    }
-                ]
-            ],
-            [
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-                        "type": "not_place",
-                        "entity": [
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-                    }
-                ]
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-                        "type": "not_place",
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-                        ],
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-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
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-                        ],
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-                            "city"
-                        ],
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-                        "dist": "1"
-                    }
-                ]
-            ],
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-                        ],
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-                        ],
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-                ]
-            ],
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-                        "B": [
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-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        ],
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-                ]
-            ],
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-                        "A": [
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-                            "tea"
-                        ],
-                        "B": [
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-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "not_place",
-                        "entity": [
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-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
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-                        "type": "not_place",
-                        "entity": [
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-                        ],
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-                    }
-                ]
-            ],
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-                        "A": [
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-                        ],
-                        "B": [
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-                            "camping"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                        ],
-                        "B": [
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-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                            "artist"
-                        ],
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-                            "april"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                            "mar"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
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-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "same_house",
-                        "A": [
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-                            "coffee"
-                        ],
-                        "B": [
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-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "april"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x3-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "drink",
-                            "tea"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x2-32": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "high school"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "education",
-                            "master"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "cooking"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "hobby",
-                            "gardening"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "associate"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "bachelor"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "painting"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "high school"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "cooking"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x6-5": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "horse"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "white"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
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-    "lgp-test-5x2-4": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "swede"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "dane"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "german"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x2-3": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-25": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "food",
-                            "stew"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "food",
-                            "stir fry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "short"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-4x4-37": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "cigar",
-                            "dunhill"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 4
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x3-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "honda civic"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "ford f150"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x6-31": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "tall"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "biography"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "cherry"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "birthday",
-                            "feb"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "height",
-                            "verytall"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "smoothie",
-                            "lime"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cherry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "jan"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "romance"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "average"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "lime"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "verytall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blue"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "watermelon"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "biography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "veryshort"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "white"
-                    ],
-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                        "desert"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "feb"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "fantasy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dragonfruit"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "mystery"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "short"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
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-    "lgp-test-6x6-22": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "occupation",
-                            "artist"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "occupation",
-                            "doctor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "purple"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "color",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "red"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "color",
-                            "green"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "nurse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cultural"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x2-28": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "bella"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "children",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "timothy"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "children",
-                            "meredith"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "bella"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "samantha"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "fred"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "alice"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-3x4-1": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-27": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "vacation",
-                            "city"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "teacher"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "rock"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "hip hop"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-2": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "children",
-                            "alice"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "average"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "children",
-                            "meredith"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "children",
-                            "samantha"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "bob"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "alice"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-26": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "may"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "carol"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "housestyle",
-                            "mediterranean"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "eric"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "victorian"
-                        ],
-                        "B": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "housestyle",
-                            "colonial"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "fish"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "birthday",
-                            "april"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "modern"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "birthday",
-                            "mar"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "mediterranean"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "colonial"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "victorian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "craftsman"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "modern"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "housestyle",
-                        "ranch"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x5-34": {
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
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-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "tesla model 3"
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-                    }
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-            ],
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-                        "type": "same_house",
-                        "A": [
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-                            "alice"
-                        ],
-                        "B": [
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-                            "samsung galaxy s21"
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-                        "A": [
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-                            "xiaomi mi 11"
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-                            "blue master"
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-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "cigar",
-                            "prince"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "ford f150"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "swede"
-                        ],
-                        "B": [
-                            "cigar",
-                            "yellow monster"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "chevrolet silverado"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "prince"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "iphone 13"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "brit"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dunhill"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "huawei p50"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ford f150"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dane"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "yellow monster"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "xiaomi mi 11"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "norwegian"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "pall mall"
-                    ],
-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                        "google pixel 6"
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-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                    "pos": 5
-                },
-                {
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-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                        "samsung galaxy s21"
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-                    "pos": 5
-                },
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-                    "type": "place",
-                    "entity": [
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-                        "honda civic"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "swede"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blends"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "oneplus 9"
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bmw 3 series"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "german"
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-                    "pos": 6
-                }
-            ]
-        ]
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-    "lgp-test-6x5-27": {
-        "clue_irs": [
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "bachelor"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "B": [
-                            "education",
-                            "associate"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "not_place",
-                        "entity": [
-                            "birthday",
-                            "sept"
-                        ],
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-                    }
-                ]
-            ],
-            [
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-                        "A": [
-                            "carmodel",
-                            "bmw 3 series"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "birthday",
-                            "jan"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "artist"
-                        ],
-                        "B": [
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-                            "doctorate"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "ford f150"
-                        ],
-                        "B": [
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-                            "engineer"
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-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                            "trade school"
-                        ],
-                        "B": [
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-                            "eric"
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-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                            "trade school"
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-                        "B": [
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-                            "bachelor"
-                        ],
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-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "may"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "bmw 3 series"
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-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                            "chevrolet silverado"
-                        ],
-                        "B": [
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-                            "alice"
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-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                        "B": [
-                            "name",
-                            "bob"
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-                        "dist": "1"
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-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
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-                ]
-            ],
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-                        "A": [
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-                        "A": [
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-                ]
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-                ]
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-                            "nurse"
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-                        "dist": "1"
-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
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-                            "teacher"
-                        ],
-                        "B": [
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-                        ]
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-                ]
-            ],
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-                        "A": [
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-                            "toyota camry"
-                        ],
-                        "B": [
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-                            "honda civic"
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-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
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-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ]
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                },
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-                    ],
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-                },
-                {
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-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "jan"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
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-                },
-                {
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-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 4
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "honda civic"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "high school"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "artist"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "chevrolet silverado"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "education",
-                        "doctorate"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "bmw 3 series"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "may"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "mystery"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "science fiction"
-                        ],
-                        "B": [
-                            "children",
-                            "bella"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "children",
-                            "meredith"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "children",
-                            "fred"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "children",
-                            "fred"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "romance"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "children",
-                            "timothy"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "science fiction"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "bookgenre",
-                            "fantasy"
-                        ],
-                        "B": [
-                            "mother",
-                            "penny"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "fred"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "mystery"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "meredith"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "science fiction"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "bella"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "romance"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "timothy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "fantasy"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "children",
-                        "samantha"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "bookgenre",
-                        "biography"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-10": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "food",
-                            "soup"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "root beer"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "stir fry"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "grilled cheese"
-                        ],
-                        "B": [
-                            "height",
-                            "tall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "phonemodel",
-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "supertall"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "pizza"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "food",
-                            "soup"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "height",
-                            "verytall"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "supertall"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "fish"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stir fry"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "verytall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "soup"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "stew"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "supertall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "boba tea"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "spaghetti"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "rabbit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "pizza"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "short"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "root beer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "food",
-                        "grilled cheese"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "coffee"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "hamster"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x4-38": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "occupation",
-                            "engineer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "lawyer"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
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-                        "type": "place",
-                        "entity": [
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-                            "dane"
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
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-                        ],
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
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-                        ],
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-                        "dist": "1"
-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "lilies"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
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-                        "dist": "?"
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-                ]
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-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
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-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "flower",
-                            "lilies"
-                        ],
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "teacher"
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-                    }
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-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
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-                    ],
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-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tulips"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "german"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "teacher"
-                    ],
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-                },
-                {
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-                    "entity": [
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-                        "peter"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "artist"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "lilies"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "norwegian"
-                    ],
-                    "pos": 4
-                },
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-                    "type": "place",
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "daffodils"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "swede"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "engineer"
-                    ],
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-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-34": {
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-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "food",
-                            "spaghetti"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "place",
-                        "entity": [
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-                            "lime"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "carol"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
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-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "engineer"
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-                    }
-                ]
-            ],
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-                        "type": "place",
-                        "entity": [
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-                    }
-                ]
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                            "dog"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "food",
-                            "pizza"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
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-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "desert"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "pos_relation",
-                        "A": [
-                            "occupation",
-                            "nurse"
-                        ],
-                        "B": [
-                            "food",
-                            "spaghetti"
-                        ],
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-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "smoothie",
-                            "cherry"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                            "cherry"
-                        ],
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-                            "desert"
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-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
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-                        "A": [
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-                        ],
-                        "direction": "any",
-                        "dist": 2
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-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                        ],
-                        "B": [
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-                            "stew"
-                        ],
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-                    }
-                ]
-            ],
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-                        "A": [
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-                        ],
-                        "B": [
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-                ]
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-                        "type": "same_house",
-                        "A": [
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-                            "occupation",
-                            "teacher"
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-                        "type": "pos_relation",
-                        "A": [
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-                            "engineer"
-                        ],
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-                            "rock"
-                        ],
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-                ]
-            ],
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-                        "type": "not_place",
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-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                        "B": [
-                            "pet",
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-                ]
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-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "blueberry"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
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-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "cat"
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-                        "type": "not_place",
-                        "entity": [
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-                        "pos": 6
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-                ]
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-                        "type": "not_place",
-                        "entity": [
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-                        "pos": 2
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-                ]
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
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-                        "pos": 4
-                    }
-                ]
-            ]
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-                    "type": "place",
-                    "entity": [
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-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "pizza"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cat"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
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-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    ],
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-                },
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-                },
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-                    "pos": 2
-                },
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-                },
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-                },
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-                },
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-                },
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-                },
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-                },
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-                },
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-                },
-                {
-                    "type": "place",
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-                    "pos": 4
-                },
-                {
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-                },
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-                },
-                {
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-                },
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-                },
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-                },
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-                    ],
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-                },
-                {
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-                },
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-                },
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-                },
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-                    ],
-                    "pos": 6
-                },
-                {
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-                    ],
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-                },
-                {
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-                    ],
-                    "pos": 6
-                },
-                {
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-                }
-            ]
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "carmodel",
-                            "honda civic"
-                        ],
-                        "B": [
-                            "phonemodel",
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-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
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-                        "A": [
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-                            "google pixel 6"
-                        ],
-                        "B": [
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-                            "basketball"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "iphone 13"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
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-                            "ford f150"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
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-                        ]
-                    }
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-            ],
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-                        "type": "place",
-                        "entity": [
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-                            "lilies"
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-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "peter"
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-                        "B": [
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-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
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-                        "A": [
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-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
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-                ]
-            ],
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "carnations"
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-                        "pos": 4
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
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-                        "B": [
-                            "flower",
-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "carmodel",
-                            "toyota camry"
-                        ],
-                        "B": [
-                            "carmodel",
-                            "tesla model 3"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tennis"
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "iphone 13"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "honda civic"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
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-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
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-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
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-                    "pos": 2
-                },
-                {
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-                    "entity": [
-                        "carmodel",
-                        "toyota camry"
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-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                    "pos": 2
-                },
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-                    "entity": [
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "soccer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "carmodel",
-                        "tesla model 3"
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
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-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "swimming"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "oneplus 9"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "ford f150"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "roses"
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-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "craftsman"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
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-                ]
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-            [
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-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
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-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "desert"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "colonial"
-                        ]
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-                ]
-            ],
-            [
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-                        "A": [
-                            "smoothie",
-                            "watermelon"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
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-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                            "cherry"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "arnold"
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-                        "B": [
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-                            "tea"
-                        ]
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-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
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-                            "colonial"
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-                        "entity": [
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-                    }
-                ]
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-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "colonial"
-                        ],
-                        "B": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "housestyle",
-                            "ranch"
-                        ],
-                        "B": [
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-                            "milk"
-                        ]
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-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
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-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
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-                        ],
-                        "B": [
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-                            "lilies"
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-                    }
-                ]
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-                    "entity": [
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-                    "pos": 1
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-                },
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-                    "entity": [
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-                },
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-                    "entity": [
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-                },
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-                {
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-                {
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-                {
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-                        "B": [
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-                            "tennis"
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-                            "tennis"
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-                        "A": [
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-                            "bob"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
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-                        "type": "not_place",
-                        "entity": [
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-                        "A": [
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-                        "B": [
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-                            "beach"
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-                        "type": "same_house",
-                        "A": [
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-                            "cruise"
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-                        "A": [
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-                            "bob"
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-                        "B": [
-                            "education",
-                            "associate"
-                        ]
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-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
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-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
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-                        "type": "pos_relation",
-                        "A": [
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-                            "camping"
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-                        "B": [
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-                            "city"
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-                        "dist": 1
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-                ]
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-                        "type": "same_house",
-                        "A": [
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-                            "eric"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "swimming"
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-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "basketball"
-                        ],
-                        "B": [
-                            "vacation",
-                            "mountain"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                            "tennis"
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-                        "B": [
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-                        "dist": "?"
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-                        "type": "same_house",
-                        "A": [
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-                        ],
-                        "B": [
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-                            "soccer"
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-                },
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-                },
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-                },
-                {
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-                    "entity": [
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-                        "huawei p50"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
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-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                }
-            ]
-        ]
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-    "lgp-test-5x4-12": {
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-                ]
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-                ]
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-                    }
-                ]
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-                ]
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "smoothie",
-                            "dragonfruit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "beach"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "watermelon"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "city"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "fish"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "cherry"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "mountain"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "lime"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "beach"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "dragonfruit"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "camping"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "smoothie",
-                        "desert"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-38": {
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-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "arnold"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "name",
-                            "peter"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "musicgenre",
-                            "classical"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "musicgenre",
-                            "pop"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "hip hop"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "classical"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "musicgenre",
-                            "jazz"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "coffee"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "rock"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "tea"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "hip hop"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "root beer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "classical"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "pop"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "musicgenre",
-                        "jazz"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x4-33": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "short"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "brit"
-                        ],
-                        "pos": 6
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "nationality",
-                            "german"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "bob"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "red"
-                        ],
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-                    }
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "supertall"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "height",
-                            "average"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
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-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "nationality",
-                            "dane"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ]
-        ],
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-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                        "german"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "veryshort"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "norwegian"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "supertall"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dane"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "short"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "swede"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "auburn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "chinese"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "average"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "nationality",
-                        "brit"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-39": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "mar"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "birthday",
-                            "feb"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "doctor"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "occupation",
-                            "artist"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "penny"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "occupation",
-                            "teacher"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "B": [
-                            "birthday",
-                            "jan"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "holly"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "peter"
-                        ],
-                        "B": [
-                            "occupation",
-                            "lawyer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "birthday",
-                            "sept"
-                        ],
-                        "B": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "gray"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "feb"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "penny"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "doctor"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "sept"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "lawyer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "black"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "april"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "engineer"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "jan"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "aniya"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "artist"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "birthday",
-                        "mar"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "occupation",
-                        "teacher"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "gray"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x5-34": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "red"
-                        ],
-                        "B": [
-                            "pet",
-                            "bird"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "pet",
-                            "cat"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "average"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "height",
-                            "veryshort"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "verytall"
-                        ],
-                        "B": [
-                            "mother",
-                            "janelle"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "mother",
-                            "penny"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "hamster"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "mother",
-                            "aniya"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "pet",
-                            "dog"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "mother",
-                            "kailyn"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "bird"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "bob"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "hamster"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "gray"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "penny"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "fish"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "brown"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "height",
-                        "tall"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "holly"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "peter"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cat"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blonde"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "janelle"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "haircolor",
-                        "red"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "veryshort"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "mother",
-                        "kailyn"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "black"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "verytall"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "aniya"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-5x3-14": {
-        "clue_irs": [
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "name",
-                            "bob"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "red"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "alice"
-                        ],
-                        "B": [
-                            "color",
-                            "yellow"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "name",
-                            "arnold"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "green"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "pall mall"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "alice"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
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-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 5
-                }
-            ]
-        ]
-    },
-    "lgp-test-6x6-30": {
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-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "nationality",
-                            "german"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "white"
-                        ],
-                        "B": [
-                            "drink",
-                            "coffee"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "education",
-                            "bachelor"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "water"
-                        ],
-                        "B": [
-                            "color",
-                            "purple"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "B": [
-                            "color",
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-                        ]
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "education",
-                            "high school"
-                        ]
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-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "iris"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "associate"
-                        ],
-                        "B": [
-                            "color",
-                            "green"
-                        ]
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-            ],
-            [
-                [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "nationality",
-                            "chinese"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "red"
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-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "alice"
-                        ],
-                        "B": [
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-                            "swede"
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-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "brit"
-                        ],
-                        "B": [
-                            "nationality",
-                            "chinese"
-                        ],
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-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
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-                            "bachelor"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "color",
-                            "yellow"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "milk"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "education",
-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "same_house",
-                        "A": [
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-                            "swede"
-                        ],
-                        "B": [
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-                            "master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "pos_relation",
-                        "A": [
-                            "education",
-                            "trade school"
-                        ],
-                        "B": [
-                            "nationality",
-                            "chinese"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "place",
-                        "entity": [
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-                            "german"
-                        ],
-                        "pos": 5
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "nationality",
-                            "norwegian"
-                        ],
-                        "B": [
-                            "drink",
-                            "water"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
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-                        "eric"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "dane"
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-                    "pos": 1
-                },
-                {
-                    "type": "place",
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-                        "daffodils"
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-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
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-                },
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-                    "entity": [
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-                        "trade school"
-                    ],
-                    "pos": 1
-                },
-                {
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-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                    "pos": 2
-                },
-                {
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-                    "entity": [
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-                },
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-                },
-                {
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-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                },
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-                },
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-                },
-                {
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "chinese"
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-                },
-                {
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-                    "pos": 4
-                },
-                {
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-                },
-                {
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-                    "entity": [
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-                },
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-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                },
-                {
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-                    "entity": [
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-                },
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-                    "entity": [
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-                        "tea"
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "yellow"
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-                    "pos": 5
-                },
-                {
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-                    "entity": [
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-                        "doctorate"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "norwegian"
-                    ],
-                    "pos": 6
-                },
-                {
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-                    "entity": [
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-                        "carnations"
-                    ],
-                    "pos": 6
-                },
-                {
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-                    "entity": [
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-                        "water"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "purple"
-                    ],
-                    "pos": 6
-                },
-                {
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-                    "entity": [
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-                        "high school"
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-                }
-            ]
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-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "camping"
-                        ],
-                        "B": [
-                            "hobby",
-                            "cooking"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "baseball"
-                        ],
-                        "B": [
-                            "hobby",
-                            "photography"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "B": [
-                            "vacation",
-                            "city"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "tennis"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "dog"
-                        ],
-                        "B": [
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-                            "swimming"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
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-                        "A": [
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-                            "photography"
-                        ],
-                        "B": [
-                            "drink",
-                            "tea"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                        ],
-                        "B": [
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-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "knitting"
-                        ],
-                        "B": [
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-                            "horse"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "coffee"
-                        ],
-                        "B": [
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-                            "soccer"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "mountain"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "drink",
-                            "boba tea"
-                        ],
-                        "pos": 4
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "cat"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "vacation",
-                            "beach"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "drink",
-                            "coffee"
-                        ],
-                        "B": [
-                            "name",
-                            "alice"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "drink",
-                            "tea"
-                        ],
-                        "B": [
-                            "pet",
-                            "fish"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "drink",
-                            "milk"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "rabbit"
-                        ],
-                        "B": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "direction": "any",
-                        "dist": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
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-                            "cooking"
-                        ],
-                        "pos": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "tennis"
-                        ],
-                        "B": [
-                            "pet",
-                            "rabbit"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "pet",
-                            "dog"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "hobby",
-                            "woodworking"
-                        ],
-                        "B": [
-                            "pet",
-                            "dog"
-                        ]
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-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "hobby",
-                            "painting"
-                        ],
-                        "B": [
-                            "pet",
-                            "horse"
-                        ],
-                        "direction": "any",
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-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "drink",
-                            "root beer"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "cat"
-                    ],
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-                },
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-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "volleyball"
-                    ],
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-                },
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
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-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "tennis"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "city"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "milk"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "fish"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "photography"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
-                    "type": "place",
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-                        "vacation",
-                        "beach"
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-                },
-                {
-                    "type": "place",
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "dog"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "woodworking"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "cultural"
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
-                        "water"
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "horse"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "vacation",
-                        "cruise"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "drink",
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-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "pet",
-                        "bird"
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "hobby",
-                        "gardening"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "root beer"
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-                }
-            ]
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-    "lgp-test-6x6-4": {
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-            [
-                [
-                    {
-                        "type": "not_place",
-                        "entity": [
-                            "flower",
-                            "lilies"
-                        ],
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "auburn"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "arnold"
-                        ],
-                        "B": [
-                            "vacation",
-                            "camping"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "haircolor",
-                            "auburn"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "vacation",
-                            "cultural"
-                        ],
-                        "B": [
-                            "height",
-                            "supertall"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "haircolor",
-                            "gray"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "tall"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "brown"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "craftsman"
-                        ]
-                    }
-                ]
-            ],
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-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "height",
-                            "veryshort"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "blonde"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "height",
-                            "verytall"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "roses"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ],
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-                        "dist": 3
-                    }
-                ]
-            ],
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-                    {
-                        "type": "not_place",
-                        "entity": [
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-                    }
-                ]
-            ],
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-                    {
-                        "type": "same_house",
-                        "A": [
-                            "vacation",
-                            "city"
-                        ],
-                        "B": [
-                            "height",
-                            "short"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "colonial"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                        "B": [
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-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
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-                            "red"
-                        ],
-                        "B": [
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-                            "lilies"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "mountain"
-                        ],
-                        "B": [
-                            "housestyle",
-                            "victorian"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
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-                            "daffodils"
-                        ],
-                        "B": [
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-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "A": [
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-                        ],
-                        "B": [
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-                            "average"
-                        ]
-                    }
-                ]
-            ],
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-                        "type": "not_place",
-                        "entity": [
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-                        ],
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-                    }
-                ]
-            ],
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-                        "type": "not_place",
-                        "entity": [
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-                        "pos": 5
-                    }
-                ]
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-                        "entity": [
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-                        ],
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-                    }
-                ]
-            ],
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-                        "type": "pos_relation",
-                        "A": [
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-                            "carol"
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-                        "B": [
-                            "name",
-                            "bob"
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-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
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-                        "type": "same_house",
-                        "A": [
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-                            "verytall"
-                        ],
-                        "B": [
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-                    }
-                ]
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-            [
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-                    {
-                        "type": "same_house",
-                        "A": [
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-                            "mediterranean"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "red"
-                        ]
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-                ]
-            ],
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-                        "type": "same_house",
-                        "A": [
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-                            "supertall"
-                        ],
-                        "B": [
-                            "haircolor",
-                            "black"
-                        ]
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-                ]
-            ],
-            [
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-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ]
-                    }
-                ]
-            ],
-            [
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-                        "type": "pos_relation",
-                        "A": [
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-                            "mountain"
-                        ],
-                        "B": [
-                            "vacation",
-                            "cruise"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
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-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
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-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "auburn"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                        "daffodils"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
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-                        "cruise"
-                    ],
-                    "pos": 2
-                },
-                {
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-                },
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-                    "entity": [
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-                },
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-                },
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-                    "entity": [
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-                        "bob"
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-                },
-                {
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-                    ],
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-                },
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-                        "cultural"
-                    ],
-                    "pos": 3
-                },
-                {
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-                    "entity": [
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-                },
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-                },
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                    ],
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-                },
-                {
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-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
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-                },
-                {
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-                    "entity": [
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-                },
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-                },
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-                    "entity": [
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-                },
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-                    "entity": [
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-                },
-                {
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-                    ],
-                    "pos": 5
-                },
-                {
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-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
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-                },
-                {
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-                    "pos": 6
-                },
-                {
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-                },
-                {
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-                    "entity": [
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-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
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-                }
-            ]
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-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "pos": 2
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
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-                            "xiaomi mi 11"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "flower",
-                            "carnations"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "purple"
-                        ],
-                        "B": [
-                            "cigar",
-                            "pall mall"
-                        ],
-                        "direction": "left",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "green"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "color",
-                            "yellow"
-                        ],
-                        "B": [
-                            "color",
-                            "blue"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "samsung galaxy s21"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "flower",
-                            "daffodils"
-                        ],
-                        "direction": "any",
-                        "dist": 3
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "prince"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "basketball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "volleyball"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "swimming"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "huawei p50"
-                        ],
-                        "B": [
-                            "color",
-                            "white"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "oneplus 9"
-                        ],
-                        "B": [
-                            "flower",
-                            "roses"
-                        ],
-                        "direction": "any",
-                        "dist": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "iris"
-                        ],
-                        "B": [
-                            "name",
-                            "eric"
-                        ],
-                        "direction": "left",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "cigar",
-                            "dunhill"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "color",
-                            "blue"
-                        ],
-                        "B": [
-                            "name",
-                            "peter"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "bob"
-                        ],
-                        "B": [
-                            "flower",
-                            "tulips"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "place",
-                        "entity": [
-                            "name",
-                            "alice"
-                        ],
-                        "pos": 1
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "favoritesport",
-                            "baseball"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blue master"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "phonemodel",
-                            "google pixel 6"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "direction": "right",
-                        "dist": "?"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "carol"
-                        ],
-                        "B": [
-                            "favoritesport",
-                            "soccer"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "pos_relation",
-                        "A": [
-                            "flower",
-                            "carnations"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ],
-                        "direction": "left",
-                        "dist": "1"
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "name",
-                            "eric"
-                        ],
-                        "B": [
-                            "cigar",
-                            "blends"
-                        ]
-                    }
-                ]
-            ],
-            [
-                [
-                    {
-                        "type": "same_house",
-                        "A": [
-                            "favoritesport",
-                            "volleyball"
-                        ],
-                        "B": [
-                            "phonemodel",
-                            "iphone 13"
-                        ]
-                    }
-                ]
-            ]
-        ],
-        "solution_irs": [
-            [
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "alice"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "samsung galaxy s21"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "yellow monster"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "iris"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "red"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "baseball"
-                    ],
-                    "pos": 1
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "carol"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "oneplus 9"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blue master"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "carnations"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "green"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "soccer"
-                    ],
-                    "pos": 2
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "eric"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "xiaomi mi 11"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "blends"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "roses"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "yellow"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "tennis"
-                    ],
-                    "pos": 3
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "peter"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "iphone 13"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "dunhill"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "lilies"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "blue"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "volleyball"
-                    ],
-                    "pos": 4
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "arnold"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "huawei p50"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "prince"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "daffodils"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "purple"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "basketball"
-                    ],
-                    "pos": 5
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "name",
-                        "bob"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "phonemodel",
-                        "google pixel 6"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "cigar",
-                        "pall mall"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "flower",
-                        "tulips"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "color",
-                        "white"
-                    ],
-                    "pos": 6
-                },
-                {
-                    "type": "place",
-                    "entity": [
-                        "favoritesport",
-                        "swimming"
-                    ],
-                    "pos": 6
-                }
-            ]
-        ]
-    }
-}
\ No newline at end of file
diff --git a/interwhen/utils/zebralogic_helper.py b/interwhen/utils/zebralogic_helper.py
deleted file mode 100644
index cde8a55b..00000000
--- a/interwhen/utils/zebralogic_helper.py
+++ /dev/null
@@ -1,284 +0,0 @@
-"""
-Prompt and dataset utilities for WildEval/ZebraLogic.
-"""
-
-import re
-import json
-from collections import defaultdict
-from typing import Dict, List, Tuple, Optional, Set
-from importlib import resources
-import datasets
-
-
-# ============== Prompt Templates ==============
-
-SYSTEM_PROMPT_VANILLA = """\
-# Problem Description
-
-You are solving a house grid problem. You are given:
-1. Features and Domains
-    - A fixed number of houses, indexed sequentially (e.g., House 1, House 2, …) from left to right.
-    - A set of features (e.g., color, name, pet, book genre).
-    - Each feature has a finite domain of possible values.
-2. Constraint:
-    - Each house has exactly one value per feature.
-    - No two houses share the same value for the same feature.
-3. Clues / Constraints descrbing:
-    - Houses and their positions
-    - Feature values
-    - Relative ordering (e.g., "next to", "to the left of", "2 houses away from")
-
-Solve to your best ability the arrangement of features across the houses.
-
-# Final Answer Format
-
-```json
-{
-    "House 1": { "feature1": "value1", "feature2": "value2", ... },
-    "House 2": { "feature1": "value1", "feature2": "value2", ... },
-    ...
-}
-```
-
-Make sure to use the exact feature/value names as given in the problem description.
-Make sure the JSON is valid and parsable."""
-
-SYSTEM_PROMPT_STATEPOLL = """\
-# Problem Description
-
-You are solving a house grid problem. You are given:
-1. Features and Domains
-    - A fixed number of houses, indexed sequentially (e.g., House 1, House 2, …) from left to right.
-    - A set of features (e.g., color, name, pet, book genre).
-    - Each feature has a finite domain of possible values.
-2. Constraint:
-    - Each house has exactly one value per feature.
-    - No two houses share the same value for the same feature.
-3. Clues / Constraints describing:
-    - Houses and their positions
-    - Feature values
-    - Relative ordering (e.g., "next to", "to the left of", "2 houses away from")
-
-# Rules for Solving
-
-1. Reason about the problem in text.
-2. After every inference, no matter how minor or tentative, immediately report the updated partial assignments.
-    - Always output partial assignments frequently as the reasoning progresses, not only at major steps or when confident.
-    - If an inference adds, removes, or narrows even a single possibility, report it.
-
-# House/Feature Partial Assignment Reporting Format
-
-```json
-{
-    "House N": { "feature1": "value1", "feature2": "value2", ... },
-    ...
-}
-```
-
-Omit any unassigned features.
-Make sure to use the exact feature/value names as given in the problem description.
-Make sure the JSON is valid and parsable."""
-
-SYSTEM_PROMPT_STATEFEEDBACK = """\
-# Problem Description
-
-You are solving a house grid problem. You are given:
-1. Features and Domains
-    - A fixed number of houses, indexed sequentially (e.g., House 1, House 2, …) from left to right.
-    - A set of features (e.g., color, name, pet, book genre).
-    - Each feature has a finite domain of possible values.
-2. Constraint:
-    - Each house has exactly one value per feature.
-    - No two houses share the same value for the same feature.
-3. Clues / Constraints describing:
-    - Houses and their positions
-    - Feature values
-    - Relative ordering (e.g., "next to", "to the left of", "2 houses away from")
-
-# Rules for Solving
-
-1. Reason about the problem in text.
-2. You may receive feedback from the user if anything is wrong. Use any feedback to guide your reasoning until a complete solution is reached.
-3. Do not stop responding until you've assigned each and every variable.
-
-# Final Answer Reporting Format
-
-```json
-{
-    "House 1": { "feature1": "value1", "feature2": "value2", ... },
-    "House 2": { "feature1": "value1", "feature2": "value2", ... },
-    ...
-}
-```
-
-Make sure to use the exact feature/value names as given in the problem description.
-Make sure the JSON is valid and parsable."""
-
-USER_PROMPT_TEMPLATE = "{problem_text}"
-
-# ============== Dataset Loading ==============
-
-def clean_problem_text(problem_text: str, features: dict) -> str:
-    """Clean up problem text giving explicit feature domains."""
-    desc, clues = problem_text.split('## clues:')
-    line0 = desc.splitlines()[0]
-
-    feature_text = ''
-    for feature, values in features.items():
-        values_str = ', '.join(f"'{v}'" for v in values)
-        feature_text += f"- '{feature}': {values_str}\n"
-
-    return f"{line0}\n{feature_text}\n## clues:{clues}".strip()
-
-
-def process_zebralogic_problem(problem: dict, ir_map: dict) -> dict:
-    """Process a raw ZebraLogic problem into the format needed by ZebraLogicProblem.
-
-    Args:
-        problem: Raw problem dict from the HuggingFace dataset.
-        ir_map: Dict mapping problem IDs to their IR representations.
-
-    Returns:
-        Processed problem dict with keys: n_houses, n_features, features, clues,
-        clue_irs, solution_irs, solution, puzzle_clean, etc.
-    """
-    def apply_text_replacements(problem):
-        replacements = [
-            ['january', 'jan'], ['february', 'feb'], ['march', 'mar'],
-            ['august', 'aug'], ['september', 'sept'], ['f-150', 'f150'],
-            ['animal', 'pet'], ['loves the spaghetti eater', 'loves spaghetti'],
-            ['very short', 'veryshort'], ['super short', 'supershort'],
-            ['very tall', 'verytall'], ['super tall', 'supertall'],
-        ]
-        problem_str = json.dumps(problem)
-        for old, new in replacements:
-            problem_str = problem_str.replace(old, new)
-        return json.loads(problem_str)
-
-    pid = problem['id']
-    size = problem["size"]
-    n_houses, n_features = map(int, size.split("*"))
-
-    problem_text = problem["puzzle"].lower()
-    clues_raw = re.split(r"##\s*clues\s*:", problem_text, flags=re.IGNORECASE)[1].strip().split("\n")
-    clues = []
-    for clue in clues_raw:
-        clue_text_index, clue_text = clue.strip().split(". ", 1)
-        clues.append({
-            "text_index": int(clue_text_index.strip()),
-            "text": clue_text.strip()
-        })
-
-    solution = problem["solution"]
-    solution['header'] = [h.lower() for h in solution['header']]
-    solution['rows'] = [[v.lower() for v in row] for row in solution['rows']]
-
-    features = defaultdict(list)
-    for row in solution['rows']:
-        for fname, value in zip(solution['header'], row):
-            if fname.lower() == 'house':
-                continue
-            features[fname].append(value)
-    features = dict(features)
-    for fname in features:
-        features[fname] = sorted(list(set(features[fname])))
-        assert len(features[fname]) == n_houses
-    assert len(features) == n_features
-
-    processed_solution = {f'House {i+1}': {} for i in range(n_houses)}
-    for house_i, row in enumerate(solution['rows']):
-        for fname, value in zip(solution['header'][1:], row[1:]):
-            processed_solution[f'House {house_i+1}'][fname.lower()] = value.lower()
-    problem['solution'] = processed_solution
-
-    problem['puzzle'] = problem_text
-    problem["clues"] = clues
-    problem["features"] = features
-    problem["n_houses"] = n_houses
-    problem["n_features"] = n_features
-    problem["clue_irs"] = ir_map[pid]["clue_irs"]
-    problem["solution_irs"] = ir_map[pid]["solution_irs"]
-    problem['puzzle_clean'] = clean_problem_text(problem['puzzle'], problem['features'])
-
-    return apply_text_replacements(problem)
-
-def get_zebralogic_dataset() -> list:
-    """Load and process the ZebraLogic dataset from HuggingFace.
-
-    Loads WildEval/ZebraLogic grid_mode test split and processes each problem
-    with the IR map.
-
-    The IR map file must be at interwhen/data/zebralogic_ir_map.json
-
-    Returns:
-        List of processed problem dicts.
-    """
-
-    dataset = datasets.load_dataset("WildEval/ZebraLogic", "grid_mode", split="test").to_list()
-
-    pkg = "interwhen.data"
-    with resources.files(pkg).joinpath("zebralogic_ir_map.json").open("r") as f:
-        ir_map = json.load(f)
-
-    # Known problematic problem IDs (unsolvable or malformed)
-    bad_ids = {
-        'lgp-test-6x5-2', 'lgp-test-6x6-5', 'lgp-test-2x5-1', 'lgp-test-4x5-5',
-        'lgp-test-2x4-6', 'lgp-test-2x6-11', 'lgp-test-4x6-35', 'lgp-test-3x5-15',
-        'lgp-test-5x5-37', 'lgp-test-5x5-17', 'lgp-test-4x5-15', 'lgp-test-6x6-2',
-        'lgp-test-5x6-4', 'lgp-test-5x6-2', 'lgp-test-5x5-1'
-    }
-    dataset = [p for p in dataset if p['id'] not in bad_ids]
-    dataset = [process_zebralogic_problem(p, ir_map) for p in dataset]
-    return dataset
-
-def extract_last_json(text):
-    """Extract the last JSON object from the model's output text."""
-    json_text = text.split('</think>')[-1].strip()
-    
-    # try with md tags
-    matches = re.findall(r'```json(.*?)```', json_text, re.DOTALL)
-    if matches and len(matches) > 0:
-        json_match = matches[-1]
-        return json.loads(json_match.strip())
-    
-    # try without assuming md tags
-    matches = re.findall(r'\{.*\}\s*?}', json_text, re.DOTALL)
-    if matches and len(matches) > 0:
-        json_match = matches[0]
-        return json.loads(json_match.strip())
-    
-    return None
-
-def zebra_correctness(problem: dict, candidate_solution: dict) -> Tuple[int, int, int, int]:
-    """Check candidate solution against ground truth.
-
-    Args:
-        problem: Processed problem dict with 'solution', 'n_houses', 'n_features', 'features'.
-        candidate_solution: Dict mapping "House N" -> {feature: value}.
-
-    Returns:
-        (correct, skipped, missing, total) counts where:
-            correct: Number of matching assignments
-            skipped: Assignments for invalid houses/features
-            missing: Features not in candidate solution
-            total: Total expected assignments (n_houses * n_features)
-    """
-    c, s = 0, 0
-    t_soln = 0
-    t = problem['n_houses'] * problem['n_features']
-    solution = problem['solution']
-
-    for house in candidate_solution:
-        if house not in solution:
-            s += len(problem['features'])
-            continue
-        for fname in candidate_solution[house]:
-            if fname not in solution[house]:
-                s += 1
-                continue
-            t_soln += 1
-            if candidate_solution[house][fname] == solution[house][fname]:
-                c += 1
-
-    m = t - t_soln
-    return c, s, m, t